21. Stable Algebraic Topology 1945-1966, By J.P. May This is a reasonably comprehensive treatment of the history of stable algebraic topology during the cited period. The table of contents gives an idea of the http://www.math.uiuc.edu/K-theory/0321/

Stable algebraic topology 1945-1966, by J.P. May This is a reasonably comprehensive treatment of the history of stable algebraic topology during the cited period. The table of contents gives an idea of the scope and limitations of the study. The emphasis is on the evolution of ideas, but some mathematical exposition of most of the main results is given. This paper will appear in a volume on the history of topology that is being edited by Ioan James. Contents: Setting up the foundations The Eilenberg-Steenrod axioms Stable and unstable homotopy groups Spectral sequences and calculations in homology and homotopy The introduction of cobordism The route from cobordism towards K-theory Bott periodicity and K-theory The Adams spectral sequence and Hopf invariant one S-duality and the introduction of spectra Oriented cobordism and complex cobordism K-theory, cohomology, and characteristic classes Generalized homology and cohomology theories Vector fields on spheres and J(X) Further applications and refinements of K-theory Bordism and cobordism theories Further work on cobordism and its relation to K-theory High dimensional geometric topology Iterated loop space theory Algebraic K-theory and homotopical algebra The stable homotopy category The Bibliography lists over 300 items.

22. Algebraic Topology Notes These are the notes for my first year algebraic topology Course. They are fairly rough, but you are invited to use them as you see fit. http://math.hunter.cuny.edu/~rthompso/algtop/

Rob Thompson Mathematics CUNY Graduate Center Math 70800 Topology I Spring 2008 These are the notes for the course. algtop.dvi algtop.pdf Here are the problem sets: Problem Set One, due 2/19, dvi file Problem Set One, due 2/19, pdf file Problem Set One, Solutions, pdf file Problem Set One, Solutions, dvi file ... Problems Set Two, dvi file

23. Algebraic Topology Authors/titles Recent Submissions xxx.yukawa.kyotou.ac.jp/list/math.AT/recent - a class=fl href="/search?hl=en 37 September 2001. http://xxx.yukawa.kyoto-u.ac.jp/list/math.AT/recent

jp.arXiv.org math math.AT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Algebraic Topology Authors and titles for recent submissions Thu, 13 Mar 2008 Wed, 12 Mar 2008 Tue, 11 Mar 2008 Mon, 10 Mar 2008 ... Thu, 6 Mar 2008 [ total of 8 entries: [ showing up to 25 entries per page: fewer more Thu, 13 Mar 2008 arXiv:0803.1746 (cross-list from math.GR) [ ps pdf other Title: Equivalences between fusion systems of finite groups of Lie type Authors: Carles Broto Bob Oliver Comments: 20 pages, uses diagrams.sty and xy-pic License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Subjects: Group Theory (math.GR) ; Algebraic Topology (math.AT) arXiv:0803.1666 (cross-list from math.GT) [ ps pdf other Title: Cobordism of fold maps, stably framed manifolds and immersions Authors: Boldizsar Kalmar Comments: 7 pages License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Subjects: Geometric Topology (math.GT) ; Algebraic Topology (math.AT) Wed, 12 Mar 2008 arXiv:0803.1641 (cross-list from math.KT) [ ps pdf other Title: Some remarks on Nil groups in algebraic K-theory Authors: James F. Davis

24. PMA 333 Algebraic Topology algebraic topology PMA 333. This course is taught by Neil Strickland. My office is J10 in the Hicks Building, and my internal phone number is 23852. http://neil-strickland.staff.shef.ac.uk/courses/algtop/

Algebraic Topology PMA 333 This course is taught by Neil Strickland. My office is J10 in the Hicks Building, and my internal phone number is 23852. The best way to reach me outside of lectures is by email: N.P.Strickland@sheffield.ac.uk. Lectures are at 11:10 on Tuesdays in Hicks lecture room 6, and at 11:10 on Fridays in Hicks lecture room 9. Problem sheets and solutions will appear on this web page in due course. Course information: The syllabus, recommended books, etc. Notes Pictures and animated diagrams (generated by Mathematica The plane The sphere The torus The The projective plane Curves in a plane region Curves in the complement of a circle Path lifting Odds and ends Problem sets and solutions Problem set 1 Problem set 2 Problem set 3 Problem set 4 ... Problem set 7 About the exam Guidance notes for the exam. A sample exam and solutions The 2001 exam and solutions A collection of questions taken from past papers (and edited to make them compatible with this year's course) and solutions. You are warned that the sample exam and questions from past papers have not been thoroughly debugged.

25. Algebraic Topology Notes algebraic topology Notes. Abstract homotopy theory (pdf). Classification of covering maps (pdf). From singular chains to Alexander duality (pdf) http://www.math.ku.dk/~moller/f04/algtop/AlgTopnotes.html

Algebraic Topology Notes Abstract homotopy theory ( pdf ). (Also avialable from Intute Classification of covering maps ( pdf From singular chains to Alexander duality ( pdf Last modified: Tue Feb 12 08:45:09 CET 2008

26. The Math Forum - Math Library - Algebraic Topology The Math Forum s Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites http://mathforum.org/library/topics/alg_topol/

Browse and Search the Library Home Math Topics Topology : Algebraic Topology Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Algebraic Topology - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to algebraic topology, the study of algebraic objects attached to topological spaces. The algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fibre bundles and related spaces are included here... the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> AT Algebraic Topology (Front for the Mathematics ArXiv) - Univ. of California, Davis

27. M.M.Postnikov International Mathematical Conference - Algebraic Topology: Old An V.Sharko, L^2 invariants and their application in algebraic topology. S.Stolz, Super symmetric quantum field theories and generalized cohomology, Part 2 http://at2007pm.org/

ALGEBRAIC TOPOLOGY: OLD AND NEW M.M.POSTNIKOV MEMORIAL CONFERENCE M.M.Postnikov Links: M.M.Postnikov's Tree in The Mathematics Genealogy Project M.M.Postnikov's Works Memorial Page (in Russian) M.M.Postnikov's photos          Articles about M.M.Postnikov:    Stefan Banach International Mathematical Center Bedlewo, Poland   18-24 June 2007     e-mail: at yahoo.co.uk PLENARY SPEAKERS: R.Cohen, Morse theory, Floer theory, and String Topology M.Furuta, The Pontrjagin-Thom construction and non-linear Fredholm theory S.Galatius, Spaces of graphs and manifolds S.Haller, Complex valued Ray-Singer torsion K.Ono, Floer cohomology and symplectic fixed points V.Sharko, L^2- invariants and their application in Algebraic Topology S.Stolz, Super symmetric quantum field theories and generalized cohomology, Part 2 D.Sullivan, Applications of Algebraic Analogues of Postnikov Systems to Geometry P.Teichner, Super symmetric quantum field theories and generalized cohomology, Part 1 CONFERENCE SCHEDULE The opening talk delivered by DENNIS SULLIVAN.

28. AMS Summer 1999 Research Conference In Algebraic Topology University of Colorado, Boulder, USA; 2024 June 1999. Photos, proceedings. http://www.math.wayne.edu/~rrb/Summer99/

1999 AMS-IMS-SIAM Summer Research Conference on HOMOTOPY METHODS IN ALGEBRAIC TOPOLOGY WHEN: Sunday, June 20 - Thursday, June 24, 1999 (check in June 19, check out June 25) WHERE: University of Colorado , Boulder, CO Now that the conference is over, this web page will be maintained for a time as a source of information about the conference and about the proceedings of the conference. (Which should be appearing any day now.) Here are some photos from the banquet, taken by Donna Salter of the AMS. Here is a copy of the conference photo . It is a 700500 byte jpeg, 3000 x 2187 pixels in size, which takes 10 to 20 minutes to download on my 28 K line. Note that the upper left corner is quite dark: there is nothing wrong with your browser. Scroll down and right to see the people in the photo. Here is a cropped version which is only 532849 bytes, 1265 x 436 pixels in size, and which appears much smaller for some reason known only to XV, the program used to crop it. This is the schedule of talks as they actually occurred, and an alphabetical list of speakers (with titles and abstracts), and the

29. Nonabelian Algebraic Topology AT/0212274 It will be seen from this article, that the structures which enable the full use of crossed complexes as a tool in algebraic topology are http://www.bangor.ac.uk/~mas010/nonab-a-t.html

Nonabelian algebraic topology by Ronald Brown, Philip J. Higgins and Rafael Sivera Update: January 27, 2008 The papers which give this theory were developed over the period 1971-2001. For a survey of the material to be contained in the book, see the article `Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems', Proceedings of the Fields Institute Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, September 23-28, Fields Institute Communications 43 (2004) 101-130. math.AT/0212274 It will be seen from this article, that the structures which enable the full use of crossed complexes as a tool in algebraic topology are substantial, intricate and interrrelated. Main Diagram of functors and monoidal closed categories which are exploited and need to be explained It should be emphasised that the functor P from filtered spaces to crossed complexes is defined in terms of relative homotopy groups. Its major properties can be understood and are developed without resource to singular cohomology , while nonabelian results, inaccessible to traditional methods, are obtained in dimension 2. A major result, generalising classical results of Eilenberg-Mac Lane, and using all the tools developed, is the

30. UNL | Math | Events | Special | Commutative Algebra: Connections With Algebraic The goal of this meeting is to bring together researchers from commutative algebra and those in algebraic topology and representation theory whose research http://www.math.unl.edu/events/special/lucho_fest/

var navl2Links = 0; //Default navline2 links to display (zero based counting) Skip Navigation Visitor Prospective Student Current Student Search: UNL Web UNL People Worldwide Go UNL Quick Links About UNL Academic Calendar Administrative Units Apply for Admission Colleges and Departments Gifts to Your University News Office of the Chancellor Parents Association UNL Fact Book UNL Policies UNL Today UNL Events more ... Undergraduate Admissions Graduate Studies Extended Education College of Law more ... WAM! MyUNL Schedule of Classes Libraries Student Involvement more ... ESS Human Resources The Scarlet Academic Senate Notes more ... Office of Research Technology Development Rental Space at UNL more ... Huskers Alumni Lied Center NET Ross Theatre Sheldon Gallery State Museum UofN Press Quilt Study NU Foundation NU System Go UNL Math Events ... Special Commutative Algebra: Connections with Algebraic Topology and Representation Theory Contact Us Resources Schedule of Classes People ... Math Placement Exam Department of Mathematics Join us in celebrating... Navigation Your browser does not appear to support JavaScript, or you have turned JavaScript off. You may use unl.edu without enabling JavaScript, but certain functions may not be available. Commutative Algebra: Connections with Algebraic Topology and Representation Theory A conference on the occasion of Luchezar Avramov's 60th birthday Aim The goal of this meeting is to bring together researchers from commutative algebra and those in algebraic topology and representation theory whose research draws from and contributes to commutative algebra.

31. Course 421 - Algebraic Topology The lecture notes for course 421 (algebraic topology), taught at Trinity College, Dublin, in the academic year 19981999, are available also here. http://www.maths.tcd.ie/~dwilkins/Courses/421/

Course 421 - Algebraic Topology Course 421 for the Academic Year 2006-7 The course is offered as a reading course to a limited number of students who have signed up for the course. The syllabus: All sections of the 2002-3 notes from section 2 (Homotopies and Covering maps) onwards; The topological classification of closed surfaces, from the 1998-9 lecture notes (part IV). Worked solutions to some old examinations: Annual Exam 1999 [ PDF PostScript Annual Exam 2003 [ PDF PostScript Annual Exam 2005 [ PDF PostScript Lecture Notes for the Academic Year 2002-3 The following lecture notes for the academic year 2002-3 are currently available:- Michaelmas Term 2002 DVI PDF PostScript Hilary Term 2003 DVI PDF PostScript Problem Sets for the Academic Year 2002-3 The following problems sets for the academic year 2002-3 are currently available:- Problems I DVI PDF PostScript Problems II PDF PostScript Lecture Notes for the Academic Year 1998-9 The lecture notes for course 421 ( Algebraic topology ), taught at Trinity College, Dublin, in the academic year 1998-1999, are available also here. (Note that the syllabus for the course as taught that year differs from the current syllabus.) The course consisted of four parts:- Part I: Topological Spaces DVI PDF PostScript Part II: Covering Maps and the Fundamental Group DVI PDF PostScript Part III: Simplicial Homology Theory DVI PDF PostScript Part IV: The Topological Classification of Closed Surfaces PostScript dwilkins@maths.tcd.ie

32. Michi’s Blog » Blog Archive » Introduction To Algebraic Topology And Rel Thanks for this brief introduction to algebraic topology. I’ve been curious about it, but haven’t been able to grok what it was about since most books on http://blog.mikael.johanssons.org/archive/2006/01/introduction-to-algebraic-topo

Because my LiveJournal is too silly About Login Introduction to Algebraic Topology and related topics (I) January 1st, 2006 homeomorphic , which technically means that there is an isomorphism between the objects in the category of topological spaces; and more comprehensibly means that there are continuous functions between the shapes such that they are each others inverses. By a continuous function, we mean a function such that it respects the topology Next, we say that two curves are equivalent if we can nudge the lengths of string bit by bit, staying within the space all the time, until one lies on top of the other. If we look at all equivalent curves as one single entity, we still are able to multiply curves by putting one after the other. If we have a curve, and then continue along the same curve, but backwards, we get a shape that can be contracted along its length to vanish into the point at the beginning and end. Thus, each element in the fundamental group of the circular ring can be characterised by the number of times we wind through, and in what direction. Any integer works, and by winding first 2 then 3 we end up winded 5=2+3 times, so in fact we can show this group to be isomorphic to , the group of integers under addition.

33. Algebraic Topology Although algebraic topology can be considered, by and large, as a creation of the 20th century, it has a long prehistory. It is generally considered to http://www.maths.lth.se/matematiklu/personal/jaak/Alg-Top.html

Algebraic Topology Brief historical introduction Although algebraic topology can be considered, by and large, as a creation of the 20th century, it has a long pre-history. It is generally considered to have its roots in Euler's polyhedron theorem (1752). This is the relation $$ E+F=K+2$$ where $E$ is the number of vertices, $K$ the number of edges, and $F$ the number of faces. In the first half of this century many mathematicians defined homology for more and more extended classes of topological spaces. Thus, for instance singular homology was first defined by Lefschetz in 1933. Finally, in 1945, Eilenberg and Steenrod developed an axiomatic approach to homology. It turned out that within the class of all topological spaces the Eilenberg and Steenrod axioms uniquely characterize singular homology. A parallel development took place in homotopy. Thus, higher homotopy groups were defined by Hurewicz in 1935 and their properties were developed. In the 1950's several new concepts were invented such as cobordism and $K$-theory. The course will be based mainly on Greenberg and Harper's book quoted below.

34. May, J. P.: A Concise Course In Algebraic Topology May, JP A Concise Course in algebraic topology, university press books, shopping cart, new release notification. http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/13911.ctl

Search: The University of Chicago Press Home Shopping Cart Our books: New general books New releases by subject Subject catalogs Complete index ... More search options News: Publicity blog Email notification RSS feeds Also @ Chicago: Information pages Distributed publishers Chicago Manual of Style Web site ... Chicago Digital Distribution Center or Print an order form May, J. P. A Concise Course in Algebraic Topology . 254 p., 117 line drawings. 6 x 9 1999 Series: (CLM) Chicago Lectures in Mathematics Paper $22.00sp ISBN: 978-0-226-51183-2 (ISBN-10: 0-226-51183-9) Fall 1999 Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

35. A Neighborhood Of Infinity: Algebraic Topology In Haskell But don t get too excited this isn t meant to be an introduction to algebraic topology. Instead it s a demonstration of how incredibly expressive Haskell http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html

A Neighborhood of Infinity Saturday, August 26, 2006 Algebraic Topology in Haskell On my shelf I have the book "Basic Topology" by Armstrong. After you've fought your way through 173 pages you eventually get to the section on simplicial topology and you can start playing with one of the basic tools of modern topology: homology groups . But you don't want to go through all that hassle. If you can read Haskell code then you can get there in 20 lines. But don't get too excited - this isn't meant to be an introduction to algebraic topology. Instead it's a demonstration of how incredibly expressive Haskell is. Before starting on this project I expected it to take a couple of weeks of early morning hacking and many hundreds of lines of code. It actually took a couple of hours. So the goal is this: use the standard chain complex from simplicial homology to compute the Betti numbers First we need some code to compute the rank of a matrix. As this is general purpose code I'm not counting it in my 20 line budget. It took me a little while to find a recursive implementation of this suitable for Haskell. Basically, the idea is that a zero matrix has zero rank and the following operations leave the rank of a matrix unchanged: Deleting a row of zeroes Deleting a column of zeroes Multiplying a row or column by a non-zero constant Adding one row to another.

36. Algebraic Topology Authors/titles Recent Submissions RT); algebraic topology (math.AT); Rings and Algebras (math.RA) Subjects algebraic topology (math.AT); High Energy Physics Theory (hep-th); http://aps.arxiv.org/list/math.AT/recent

aps.arXiv.org math math.AT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Algebraic Topology Authors and titles for recent submissions Thu, 13 Mar 2008 Wed, 12 Mar 2008 Tue, 11 Mar 2008 Mon, 10 Mar 2008 ... Thu, 6 Mar 2008 [ total of 8 entries: [ showing up to 25 entries per page: fewer more Thu, 13 Mar 2008 arXiv:0803.1746 (cross-list from math.GR) [ ps pdf other Title: Equivalences between fusion systems of finite groups of Lie type Authors: Carles Broto Bob Oliver Comments: 20 pages, uses diagrams.sty and xy-pic License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Subjects: Group Theory (math.GR) ; Algebraic Topology (math.AT) arXiv:0803.1666 (cross-list from math.GT) [ ps pdf other Title: Cobordism of fold maps, stably framed manifolds and immersions Authors: Boldizsar Kalmar Comments: 7 pages License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Subjects: Geometric Topology (math.GT) ; Algebraic Topology (math.AT) Wed, 12 Mar 2008 arXiv:0803.1641 (cross-list from math.KT) [ ps pdf other Title: Some remarks on Nil groups in algebraic K-theory Authors: James F. Davis

37. Illman: Equivariant Algebraic Topology EQUIVARIANT algebraic topology by Soren ILLMAN This talk covered the main parts of my thesis 5, see also 4 and 6. Our main objective is to provide the http://www.numdam.org/item?id=AIF_1973__23_2_87_0

38. Algebraic Topology - Part II DPMMS Teaching algebraic topology II. algebraic topology Part II. The Mathematics Faculty web site provides a schedule and a course summary. http://www.dpmms.cam.ac.uk/site2002/Teaching/II/AlgebraicTopology/

Department of Pure Mathematics and Mathematical Statistics DPMMS Teaching Algebraic Topology - Part II The Mathematics Faculty web site provides a schedule and a course summary Example sheets Example sheet 1 Example sheet 2 Example sheet 3 Example sheets from previous years Example sheet 1 Example sheet 2 Example sheet 3 Example sheet 1 ... Example sheet 3 and a sample solution for one of the questions Example sheet 3 supplement Example sheet 4 Corrections to example sheets - last updated 17th January 2005 Supplementary material from previous years Prof Totaro's teaching page Michaelmas 2006 Prof. Lickorish's notes 2003-04 Last modified: Mon Feb 4 11:44:10 2008 Information provided by webmaster@dpmms.cam.ac.uk

39. Dr. Michael Hopkins, MIT, Algebraic Topology And Differential Forms I algebraic topology and Differential Forms I. Dr. Michael Hopkins, MIT. Audio requires RealPlayer by RealNetworks. Begin WebCam and audio for the whole talk http://online.itp.ucsb.edu/online/mp03/hopkins1/

Schedule Jul 14, 2003 Algebraic Topology and Differential Forms I Dr. Michael Hopkins, MIT Audio requires RealPlayer by RealNetworks. Begin WebCam and audio for the whole talk: high bandwidth or medium bandwidth Or, begin audio only for the whole talk: high bandwidth or low bandwidth . (Or, right-click to download the whole audio file To begin viewing slides, click on the first slide below. (Or, view as pdf [Lecture I][ Lecture II Lecture III Lecture IV Lecture V ... Author entry (protected)

40. Mathematics 261: Algebraic Topology I algebraic topology studies topological spaces by associating to them algebraic invariants. The principal algebraic invariants considered in this course are http://www.math.duke.edu/graduate/courses/spring04/math261.html

Mathematics 261: Algebraic Topology I (Spring 2003) Instructor Bill Pardon Description This course is an introduction to algebraic topology. A rough outline is as follows: Introductory ideas Basic ideas of category theory Homotopy Homotopy of maps Fundemental group Cell complexes Van Kampen's Theorem Covering spaces Higher homotopy groups (very briefly) Homology Chain complexes Simplicial homology Singular homology Relative homology Homotopy invariance Excision Mayer-Vietoris Sequence Cellular Homology Eilenberg-Steenrod Axioms Algebraic topology studies topological spaces by associating to them algebraic invariants. The principal algebraic invariants considered in this course are the fundamental group (also known as the first homotopy group) and the homology groups. This course is a prerequisite for Math 262 (Algebraic Topology II). It is fundamental for students interested in research in Algebraic Geometry, Differential Geometry, Mathematical Physics, and Topology; it is also important for students in Algebra and in Number Theory. Prerequisites Basic algebra (Math 200 or 251) and Topology (Math 205), or consent from me.

Page 2     21-40 of 77    Back | 1  | 2  | 3  | 4  | Next 20