1. Algebraic Topology Book A complete, downloadable, introductory text on algebraic topology, by Prof. Allen Hatcher, Cornell Univ. 3rd Ed. 553 pp. with illustrations. http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Algebraic Topology What's in the Book? To get an idea you can look at the Table of Contents and the Preface Printed Version The book was published by Cambridge University Press in 2002 in both paperback and hardback editions, but only the paperback version is currently available (ISBN 0-521-79540-0). This is now in a seventh printing. Each printing contains corrections of various minor errors not yet weeded out from the earlier printings see farther down this page for a list of corrections. I have tried very hard to keep the price of the paperback version as low as possible, but it is gradually creeping upward and is now $34 in the US. Less expensive printings have been made for sale in China (Tsinghua University Press) and South Asia. A translation into Russian is underway. Electronic Version: By special arrangement with the publisher, an online version will continue to be available for free download here, subject to the terms in the . There are several different formats available: The whole book as a single rather large pdf file (3.5MB) of about 550 pages.

2. Algebraic Topology - Wikipedia, The Free Encyclopedia An encyclopedic reference containing definitions, some discussion, and an assortment of useful links to various resources concerning algebraic topology and http://en.wikipedia.org/wiki/Algebraic_topology

Algebraic topology From Wikipedia, the free encyclopedia Jump to: navigation search For the topology of pointwise convergence, see Algebraic topology (object) Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces Contents The method of algebraic invariants Results on homology Setting in category theory Applications of algebraic topology ... edit The method of algebraic invariants The goal is to take topological spaces and further categorize or classify them. An older name for the subject was combinatorial topology , implying an emphasis on how a space X was constructed from simpler ones (the modern standard tool for such construction is the CW-complex ). The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants, by mapping them, for example, to groups which have a great deal of manageable structure in a way that respects the relation of homeomorphism of spaces. This allows one to recast statements about topological spaces into statements about groups, which are often easier to prove. Two major ways in which this can be done are through fundamental groups , or more generally homotopy theory , and through homology and cohomology groups. The fundamental groups give us basic information about the structure of a topological space, but they are often

3. AMS Online Books/COLL27 algebraic topology text published by the American Mathematical Society (AMS), and available as a free download in PDF format. http://www.ams.org/online_bks/coll27/

Title List Help AMS Home AMS Bookstore Algebraic Topology by Solomon Lefschetz Publication Date: 1942 Number of Pages: 389 pp. Publisher: AMS ISBN: 0-8218-3397-9 COLL/27.E Download Individual Chapters FREE (10 files - 41.5mb) Frontmatter Title Contents Preface Introduction to General Topology Additive Groups Complexes Complexes: Products. Transformations. Subdivisions ... Endmatter Appendices Bibliography and Indexes Comments: webmaster@ams.org Privacy Statement Search the AMS

4. Algebraic Topology -- From Wolfram MathWorld algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, http://mathworld.wolfram.com/AlgebraicTopology.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Derwent Algebraic Topology Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces spheres tori circles ... links , configuration spaces, etc.) that remain invariant under both-directions continuous one-to-one homeomorphic ) transformations. The discipline of algebraic topology is popularly known as "rubber-sheet geometry" and can also be viewed as the study of disconnectivities . Algebraic topology has a great deal of mathematical machinery for studying different kinds of hole structures, and it gets the prefix "algebraic" since many hole structures are represented best by algebraic objects like groups and rings Algebraic topology originated with combinatorial topology , but went beyond it probably for the first time in the 1930s when was developed. A technical way of saying this is that algebraic topology is concerned with functors from the topological category of groups and homomorphisms . Here, the

5. 55: Algebraic Topology Encyclopedic reference for algebraic topology in Dave Rusin s Mathematical Atlas. Includes a brief history along with various links to textbooks, http://www.math.niu.edu/~rusin/known-math/index/55-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 55: Algebraic topology Introduction Algebraic topology is 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; fiber bundles and related spaces are included here, while complexes (CW-, simplicial-, ...) are treated in section 57. Finally, 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; the machinery (mostly derived from homological algebra) is powerful if rather daunting. In all cases, the "naturality" of the construction implies that a map between spaces induces a map between the groups. Thus one can show that no maps of some sort can exist between two spaces (e.g. homeomorphisms) since no corresponding group homomorphisms can exists. That is, the groups and homomorphisms offer an algebraic "obstruction" to the existence of maps. Classic applications include the nonexistence of retractions of disks to their boundary and, as a consequence, the Brouwer Fixed-Point Theorem. (Obstruction theory is, more generally, the creation of algebraic invariants whose vanishing is necessary for the existence of certain topological maps. For example a function defined on a subspace Y of a space X defines an element of a homology group; that element is zero iff the function may be extended to all of X.)

6. What Is Algebraic Topology? Introductory essay by Joe Neisendorfer, University of Rochester. http://www.math.rochester.edu/people/faculty/jnei/algtop.html

WHAT IS ALGEBRAIC TOPOLOGY? THE BEGINNINGS OF ALGEBRAIC TOPOLOGY Algebraic topology is a twentieth century field of mathematics that can trace its origins and connections back to the ancient beginnings of mathematics. For example, if you want to determine the number of possible regular solids, you use something called the Euler characteristic which was originally invented to study a problem in graph theory called the Seven Bridges of Konigsberg. Can you cross the seven bridges without retracing your steps? No and the Euler characteristic tells you so. Later, Gauss defined the so-called linking number, a precise invariant which tells you whether two circles are linked. It is called an invariant because it remains the same even if we continuously deform the geometric object. Gauss also found a relationship between the total curvature of a surface and the Euler characteristic. All of these ideas are bound together by the central idea that continuous geometric phenomena can be understood by the use of discrete invariants. The winding number of a curve illustrates two important principles of algebraic topology. First, it assigns to a geometric odject, the closed curve, a discrete invariant, the winding number which is an integer. Second, when we deform the geometric object, the winding number does not change, hence, it is called an invariant of deformation or, synomynously, an invariant of homotopy.

7. Hopf Topology Archive, Revised Version algebraic topology and related areas. (~400 articles) http://hopf.math.purdue.edu/

Hopf Topology Archive Welcome to the Hopf Topology Archive! NOTICE: Hopf has been moved to a virtual website on the Math department server. Most things should be transparent if you use http://hopf.math.purdue.edu as the URL. The FTP service will not be reactivated due to security concerns. If you experience problems, please report them to wilker@math.purdue.edu Thank you. Hopf Author/Title Search: enter author or title keyword into box below. PaperSearch The Hopf Logos The Hopf Archive, month by month listing. This archive list is current through August 2004 . Newer files may be in the proper directories but not listed on the html list. These are accessible as http://hopf.math.purdue/AuthorName <- usually last names of authors. If you have a submission that has not been announced or posted and some time has elapsed, please email Mark and Clarence (but please try the "Reload" button on your browser first. Thanks, Clarence) What's New! CW-Fest: MidWest Topology Seminar honoring Clarence Wilkerson's 60th birthday. Submitting Preprints and Uploading Preprints Latest maintained by Mark Hovey. Back issues of Mark's What's New!

8. ALGTOP-L, Algebraic Topology Listserv The primary functions of this list are providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, http://www.lehigh.edu/~dmd1/algtop.html

ALGTOP-L, Algebraic Topology listserv This listserv began as a discussion group in July 1995, and was converted to an automated moderated listserv in Sept 2007. To join the listserv go to https://lists.lehigh.edu/mailman/listinfo/algtop-l The primary functions of this listserv are providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology. This website also serves as an archive of links to websites related to algebraic topology. The Hopf archive is a preprint server for papers in algebraic topology. It is maintained by Clarence Wilkerson. Once a month, Mark Hovey posts abstracts of papers which have been added to the Hopf archive. Information about conferences Messages posted to the Discussion Group 1998-Sept. 2007 . The postings to the listserv are archived on the listserv. Anyone, including nonmembers, can read them here To obtain a list of our subscribers' e-mail addresses, you must now join the listserv, where this information is readily available. Links to home pages of algebraic topologists,

9. Front: Math.AT Algebraic Topology An archive of prepublication papers (preprints) on algebraic topology. http://front.math.ucdavis.edu/math.AT

Front for the arXiv Fri, 14 Mar 2008 Front math AT search register submit journals ... iFAQ math.AT Algebraic Topology Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) Cross-listings 13 Mar arXiv:0803.1746 Equivalences between fusion systems of finite groups of Lie type. Carles Broto , Jesper M. , Bob Oliver math.GR math.AT 13 Mar arXiv:0803.1666 Cobordism of fold maps, stably framed manifolds and immersions. Boldizsar Kalmar math.GT math.AT 12 Mar arXiv:0803.1641 Some remarks on Nil groups in algebraic K-theory. James F. Davis math.KT math.AT 12 Mar arXiv:0803.1639 Algebraic K-theory over the infinite dihedral group. James F. Davis , Qayum Khan , Andrew Ranicki math.KT math.AT 11 Mar arXiv:0803.1408 Laplaza Sets, or How to Select Coherence Diagrams for Pseudo Algebras. Thomas M. Fiore , Po Hu , Igor Kriz math.CT math.AT physics.hep-th Revisions 13 Mar arXiv:0710.5779 Geometric approach towards stable homotopy groups of spheres. The Hopf invariant. Petr M. Akhmet'ev math.AT math.GT 13 Mar arXiv:0706.3226

10. Algebraic Topology algebraic topology. Andries Brouwer, aeb@cwi.nl. v1.0, 991111. Some fragments of algebraic topology. 1. Introduction. 2. Topology http://www.win.tue.nl/~aeb/at/algtop.html

Next Previous Contents Algebraic Topology Andries Brouwer, aeb@cwi.nl Some fragments of algebraic topology. Introduction Topology 2.1 Topological spaces 2.2 Operations on topological spaces ... Next Previous Contents

11. Open Problems In Algebraic Topology Problems in algebraic topology, listed by Mark Hovey, mathematician at Wesleyan University. http://math.wesleyan.edu/~mhovey/problems/

Mark Hovey's Algebraic Topology Problem List This list of problems is designed as a resource for algebraic topologists. The problems are not guaranteed to be good in any wayI just sat down and wrote them all in a couple of days. Some of them are no doubt out of reach, and some are probably even worseuninteresting. I ask that anybody who gets anywhere on any of these problems, has some new problems to add, or has corrections to any of them, please keep me informed (mhovey@wesleyan.edu). If I mention a name in a problem, it might be good to consult that person before working too hard on the problem. However, even if the problems we work on are internal to algebraic topology, we must strive to express ourselves better. If we expect our papers to be accepted in mathematical journals with a wide audience, such as the Annals, JAMS, or the Inventiones, then we must make sure our introductions are readable by generic good mathematicians. I always think of the French, myselfI want Serre to be able to understand what my paper is about. Another idea is to think of your advisor's advisor, who was probably trained 40 or 50 years ago. Make sure your advisor's advisor can understand your introduction. Another point of view comes from Mike Hopkins, who told me that we must tell a story in the introduction. Don't jump right into the middle of it with "Let E be an E-infinity ring spectrum". That does not help our field. Here are the problems: Major problems in the field Morava K- and E-theory Elliptic cohomology Applications ... Miscellaneous Unstable modules and algebras over the Steenrod algebra (coming soon)

12. Algebraic Topology Authors/titles Recent Submissions Subjects KTheory and Homology (math.KT); algebraic topology (math.AT) RT); algebraic topology (math.AT); Rings and Algebras (math.RA) http://arxiv.org/list/math.AT/recent

arXiv.org math math.AT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages 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 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 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 Subjects: K-Theory and Homology (math.KT) ; Algebraic Topology (math.AT)

13. Algebraic Topology - Cambridge University Press In most mathematics departments at major universities one of the three or four basic firstyear graduate courses is in the subject of algebraic topology. http://books.cambridge.org/0521795400.htm

Home Catalogue Google Book Search Search this book Details Page extent: 556 pages Size: 253 x 177 mm Weight: 0.968 kg Library of Congress Dewey number: 514/.2 Dewey version: 21 LC Classification: QA612 .H42 2002 LC Subject headings: Algebraic topology Art and societyGermanyHistory Politics and cultureGermanyHistory Library of Congress Record Textbook Algebraic Topology Allen Hatcher Cornell University, New York Paperback DOI: There was also a Hardback of this title but it is no longer available Published February 2002 In stock (Stock level updated: 14:22 GMT, 14 March 2008) Textbook Lecturers can request inspection copies of this title. • Broad, readable coverage of the subject • Geometric emphasis gives students better intuition • Includes many examples and exercises Contents Reviews ' … this is a marvellous tome, which is indeed a delight to read. This book is destined to become very popular amongst students and teachers alike.' Bulletin of the Belgian Mathematical Society '… clear and concise … makes the book useful both as a basis for courses and as a reference work.' Monatshefte f¼r Mathematik '… the truly unusual abundance of instructive examples and complementing exercises is absolutely unique of such a kind … the distinctly circumspect, methodologically inductive, intuitive, descriptively elucidating and very detailed style of writing give evidence to the fact that the author's first priorities are exactly what students need when working with such a textbook, namely clarity, readability, steady motivation, guided inspiration, increasing demand, and as much self-containedness of the exposition as possible. No doubt, a very devoted and experienced teacher has been at work here, very much so to the benefit of beginners in the field of algebraic topology, instructors, and interested readers in general.' Zentralblatt MATH

14. Algebraic Topology Here are some notes for an introductory course on algebraic topology. The lectures are by John Baez, except for classes 24, which were taught by Derek Wise http://math.ucr.edu/home/baez/algebraic_topology/

Algebraic Topology John Baez, Mike Stay, Christopher Walker Winter 2007 Here are some notes for an introductory course on algebraic topology. The lectures are by John Baez, except for classes 2-4, which were taught by Derek Wise. The lecture notes are by Mike Stay Homework assigned each week was due on Friday of the next week. You can read answers to these homework problems, written by Christopher Walker The course used this book: James Munkres, Topology , 2nd edition, Prentice Hall, 1999. So, theorem numbers match those in this book whenever possible, and it's best to read these notes along with the book. We deviate from Munkres at various points. We skip many sections, and we more emphasis on concepts from category theory, especially near the end of the course. Class 1 (Jan. 5) - Sketch of how we'll use the fundamental group to prove there's no retraction from the disk to the circle. Class 2 is a functor. Class 3 (Jan. 10) - Change of basepoint. Simply-connected spaces. Covering spaces. Class 4 (Jan. 12) - Covering maps. Liftings.

15. MIT OpenCourseWare | Mathematics | 18.906 Algebraic Topology II, Spring 2006 | H Simplicial and singular homology, EilenbergSteenrod axioms. Cohomology ring, universal coefficient theorem, K?nneth theorem, plus additional toipcs to be http://ocw.mit.edu/OcwWeb/Mathematics/18-906Spring-2006/CourseHome/

skip to content Home Courses Donate ... Mathematics Algebraic Topology II 18.906 Algebraic Topology II Spring 2006 Pushout and pullback. (Image by MIT OCW.) Course Highlights This course features lecture notes and assignments Course Description In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor. Staff Instructor: Prof. Mark Behrens Course Meeting Times Lectures: Three sessions / week 1 hour / session Level Graduate Feedback Send feedback on this course. RSS Feeds Site Map Your use of the MIT OpenCourseWare site and course materials is subject to our Creative Commons License and other terms of use.

16. Barcelona Algebraic Topology Group This is the web site of the algebraic topology Team in Barcelona. Our research interests include a variety of subjects in algebraic topology, group theory, http://mat.uab.es/topalg/page_home.html

17. Mathematical Sciences Research Institute - Computational Applications Of Algebra algebraic topology provides measures for global qualitative features of Connections for Women Computational Applications of algebraic topology http://www.msri.org/calendar/programs/ProgramInfo/243/show_program

SITE MAP SEARCH SHORTCUT: Choose a Destination... Calendar Programs Workshops Summer Grad Workshops Seminars Events/Announcements Application Materials Visa Information Propose a Program Propose a Workshop Policy on Diversity MSRI Alumni Archimedes Society Why Give to MSRI Ways to Give to MSRI Donate to MSRI Planned Gifts FAQ Staff Member Directory Contact Us Directions For Visitors Pictures Library Computing SGP Streaming Video / VMath MSRI in the Media Emissary Newsletter Outlook Newsletter Subscribe to Newsletters Books, Preprints, etc. Federal Support Corporate Affiliates Sponsoring Publishers Foundation Support Academic Sponsors HOME ACTIVITIES CORP AFFILIATES ABOUT COMMUNICATIONS Calendar ... Events/Announcements Computational Applications of Algebraic Topology August 14, 2006 to December 15, 2006 at the Mathematical Sciences Research Institute, Berkeley, California Organized By: Gunnar Carlsson, Persi Diaconis, Susan Holmes, Rick Jardine, Günter M. Ziegler Algebraic topology provides measures for global qualitative features of geometric and combinatorial objects that are stable under deformations, and relatively insensitive to local details. This makes topology into a useful tool for understanding qualitative geometric and combinatorial questions. Considerable momentum has developed in recent years towards applications of algebraic topology in various contexts related to data analysis, object recognition, discrete and computational geometry, combinatorics, algorithms, and distributed computing.

18. Algebraic Topology & Concurrency A collection of preprints on the applications of algebraic topology to Computer Science, such as the use of topological techniques to formulate synchronous http://www.ipipan.gda.pl/~stefan/AlgTop/

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19. Algebraic Topology And Distributed Computing Powerpoint tutorials by Maurice Herlihy at Brown University. http://www.cs.brown.edu/~mph/topology.html

Algebraic Topology and Distributed Computing Page PowerPoint Tutorial Distributed and concurrent systems Protocols read/write memory decidability

20. MAT 539 -- Algebraic Topology algebraic topology A first Course, W. Fulton, GTM 153, Springer Verlag 1995; Topology from the Differentiable Viewpoint, J. Milnor, U. of Virginia Press http://www.math.sunysb.edu/~sorin/topology/

MAT 539 Algebraic Topology Instructor Sorin Popescu (office: Math 4-119, tel. 632-8358, e-mail sorin@math.sunysb.edu Prerequisites A basic introduction to geometry/topology, such as MAT 530 and MAT 531 Textbook Differential forms in algebraic topology , by Raoul Bott and Loring W. Tu, GTM , Springer Verlag 1982. The guiding principle of the book is to use differential forms and in fact the de Rham theory of differential forms as a prototype of all cohomology thus enabling an easier access to the machineries of algebraic topology in the realm of smooth manifolds. The material is structured around four core sections: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes, and includes also some applications to homotopy theory. Other recommended texts: Algebraic Topology: A first Course , W. Fulton, GTM , Springer Verlag 1995 Topology from the Differentiable Viewpoint , J. Milnor, U. of Virginia Press 1965 Algebraic Topology , A. Hatcher (on-line), Cambridge University Press, to appear Characteristic classes , J. Milnor and J. Stasheff, Princeton University Press 1974

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