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         Algebraic Topology:     more books (100)
  1. A User's Guide to Algebraic Topology (Mathematics and Its Applications) by C.T. Dodson, P.E. Parker, et all 1997-01-31
  2. Algebraic Topology (EMS Textbooks in Mathematics) by Tammo Tom Dieck, 2008-09-15
  3. Differential Algebraic Topology (Graduate Studies in Mathematics) by Matthias Kreck, 2010-05-04
  4. Essential Topology (Springer Undergraduate Mathematics Series) by Martin D. Crossley, 2005-07-01
  5. Algebraic Topology: A First Course (Mathematics Lecture Note Series) by Marvin J. Greenberg, John R. Harper, 1981-01-22
  6. Algebraic Topology via Differential Geometry (London Mathematical Society Lecture Note Series) by M. Karoubi, C. Leruste, 1988-01-29
  7. Lectures on algebraic topology (Mathematics lecture note series) by Marvin J Greenberg, 1967
  8. Introduction to Differential and Algebraic Topology (Texts in the Mathematical Sciences) by Yu.G. Borisovich, N.M. Bliznyakov, et all 2010-11-02
  9. Algebraic Topology by Robert M. Switzer, 2002-02-26
  10. Quadratic Forms with Applications to Algebraic Geometry and Topology (London Mathematical Society Lecture Note Series) by Albrecht Pfister, 1995-10-27
  11. Foundations of Algebraic Topology (Mathematics Series) by Samuel Eilenberg, Norman E. Steenrod, 1952-12
  12. Homology Theory: An Introduction to Algebraic Topology (Graduate Texts in Mathematics) (v. 145) by James W. Vick, 1994-01-07
  13. Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics) (v. 1) by Claire Voisin, 2008-02-04
  14. A Combinatorial Introduction to Topology by Michael Henle, 1994-03-14

41. CAT'05
Conference on algebraic topology June 27 July 1, 2005 Kraków (Cracow, Poland) . Previous quadrennial Conferences on algebraic topology
http://www.mimuw.edu.pl/~cat05/

42. Differential Forms In Algebraic Topology - Algebraic Topology Journals, Books &
Differential Forms in algebraic topology Geometry Topology. Developed from a first-year graduate course in algebraic topology, this text is an informal
http://www.springer.com/west/home/math/geometry?SGWID=4-10046-22-1256743-0

43. Dror Bar-Natan:Classes:2001-02:Algebraic Topology
Allen Hatcher s algebraic topology (free download; a paper copy is March 12, 14, Class notes for March 12th (the basic idea of algebraic topology,
http://www.math.toronto.edu/~drorbn/classes/0102/AlgTop/index.html
Dror Bar-Natan Classes
Fundamental Concepts in Algebraic Topology
Instructor: Dror Bar-Natan drorbn@math.huji.ac.il Classes: Tuesdays 12:00-14:00 at Mathematics 110 and Thursdays 12:00-14:00 at Sprintzak 213. Review sessions: Thursdays 14:00-15:00 with Boris Chorny chorny@math.huji.ac.il Office hours: Tuesdays 14:00-15:00 in my office, Mathematics 309. Agenda: Learn how algebra and topology interact in the field of Algebraic Topology. Syllabus: Prerequisites: Point set topology and some basic notions of algebra - groups, rings, etc. Reading material: (each student must have a copy) Weekly Material: (Also use the primitive Class Notes Browser March 12, 14 Class notes for March 12th (the basic idea of algebraic topology, Brouwer's theorem, the fundamental group, the fundamental group of the circle).
Homework assignment #1: Ex1.ps Ex1.png (category theory, fundamental group calculations, an application of Brouwer's theorem).
Class notes for March 14th
(the lifting property for covering spaces, the fundamental theorem of algebra, Brouwer's fixed point theorem)

44. Algebraic Topology
Math reference, an introduction to algebraic topology.
http://www.mathreference.com/at,intro.html
Algebraic Topology, An Introduction
Introduction
As the name suggests, algebraic topology is a marriage of algebra and topology. These branches of mathematics seem unrelated, yet they can be connected in several ways. For instance, a topological space S might be assigned a group G, based on the propertyies of S, in such a way that any space homeomorphic to S will be given the same group G. Therefore, two spaces that exhibit different groups cannot be homeomorphic. Proving a negative is always difficult; this is often the only way we can prove two spaces are different from each other. Consider a simple example, the line and the plane. These spaces seem different enough, yet they have the same cardinality. There are invertible functions that map the plane onto the line and back again. Perhaps one of these functions preserves open sets. Perhaps one dimension is really the same as two, when viewed from the right perspective. This isn't true of course; the plane is different from the line. But we need algebraic topology to prove it. The groups associated with these spaces (actually their compactifications) are different, and that closes the case. The first group that we will assign to a space S is its homotopy group, but before we can do that we need to know what a homotopy is.

45. Groupoids And Crossed Objects In Algebraic Topology
Groupoids and crossed objects in algebraic topology. Ronald Brown. This is an introductory survey of the passage from groups to groupoids and their higher
http://www.intlpress.com/hha/v1/n1/a1/
Groupoids and crossed objects in algebraic topology
Ronald Brown
This is an introductory survey of the passage from groups to groupoids and their higher dimensional versions, with most emphasis on calculations with crossed modules and the construction and use of homotopy double groupoids. Homology, Homotopy and Applications, Vol. 1, 1999, No. 1, pp 1-78 Available as: dvi dvi.gz ps ps.gz

46. CONTEMPORARY TRENDS IN ALGEBRAIC GEOMETRY AND ALGEBRAIC TOPOLOGY
CONTEMPORARY TRENDS IN ALGEBRAIC GEOMETRY AND algebraic topology.
http://www.worldscibooks.com/mathematics/4966.html
Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Bookshop New Titles Editor's Choice Bestsellers Book Series ... Nankai Tracts in Mathematics - Vol. 5
CONTEMPORARY TRENDS IN ALGEBRAIC GEOMETRY AND ALGEBRAIC TOPOLOGY
edited by Shiing-Shen Chern, Lei Fu (Nankai Institute of Mathematics, P R China) (Duke University, USA)
About the Editors Professor S S Chern retired from UC Berkeley and is now based in the Nankai Institute of Mathematics, which he founded in 1985. He is also the founding director of the Mathematical Science Research Institute, Berkeley (1981). He was awarded the National Science Medal in 1975 and Wolf Prize in Mathematics in 1983/4. His area of research was differential geometry where he studied the (now named) Chern characteristic classes in fibre spaces. The Chern Visiting Professorship, begun in 1996, honors the Berkeley professor emeritus widely regarded as the greatest geometer of his generation. "Chern's belief in young people and his encouragement of them had a lot to do with the spectacular growth of geometry in the second half of this century" mathematician Blaine Lawson has said. "It is not easy to find a geometer who was not for some period of time either a student or a post-doctoral fellow in the orbit of Chern. (http://math.berkeley.edu/) Professor Chern is also the editor of the book – Selected Papers of Wei-Liang Chow , also published by World Scientific Publishing.

47. Algebraic And Geometric Topology
Interests algebraic topology and its applications, TQFT s and CFT, noncommutative geometry, operads and higher dimensional categories, mapping
http://msp.warwick.ac.uk/agt/about/journal/edinterests.html
Editorial Interests
Recent Issues Volume 1, 2001 Volume 2, 2002 Volume 3, 2003 Volume 4, 2004 ... Volume 8, issue 1, 2008 The Journal About the Journal Editorial Board Editorial Interests Author Index ... GTP Author Index Editorial Board Interest Areas
Robert Oliver

93430 Villetaneuse
France
fax: email: bobol@math.univ-paris13.fr
Interests: All of algebraic topology John Etnyre
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160
USA
email: etnyre@math.upenn.edu Interests: All of geometric topology. Joan Birman Mathematics Department Columbia University New York NY 10027 USA email: jb@math.columbia.edu Interests: Classical knot theory, braid groups, mapping class groups, Artin groups, contact structures and knot theory Fred Cohen Department of Mathematics University of Rochester Rochester NY 14627 USA email: cohf@math.rochester.edu Interests: Algebraic topology, homotopy theory, cohomology of groups, braid groups, and related groups

48. Algebraic Topology
algebraic topology is the study of topological spaces using tools of an algebraic nature, such as homology groups, cohomology groups and homotopy groups.
http://jdc.math.uwo.ca/algtop/
Algebraic topology, Math 414b, Spring 2001
Algebraic topology is the study of topological spaces using tools of an algebraic nature, such as homology groups, cohomology groups and homotopy groups. It is one of the major accomplishments of twentieth century mathematics and has applications to many areas of mathematics and to other fields, such as physics, computer science, and economics. I encourage students from other departments to attend. This is a first course in algebraic topology which will introduce the invariants mentioned above, explain their basic properties and develop both methods of computation and geometric intuition. Course outline:
  • Instructor: Dan Christensen
  • E-mail: jdc@uwo.ca
  • Office: Middlesex 103b.
  • Office Phone:
  • Office Hours: to be determined.
  • Class times and location: Mondays, 11 am to 12:20 pm, and Fridays, 1:30 pm to 2:50 pm. MC107.
  • Prerequisites: Algebra I (group theory, Math 302a) and General Topology (Math 404a); or permission of instructor. (Students from other departments are welcome and should consult with me.)
  • Web page: This page is available at http://jdc.math.uwo.ca/algtop

49. Foundations Of Algebraic Topology
Both Point Set Topology and algebraic topology attempt to describe and analyze the properties of geometric objects which are invariant under continuous
http://www.sjsu.edu/faculty/watkins/algtop.htm
applet-magic.com
Thayer Watkins
Silicon Valley
USA Foundations of Algebraic Topology
The Nature of Algebraic Topology
Both Point Set Topology and Algebraic Topology attempt to describe and analyze the properties of geometric objects which are invariant under continuous mappings. Algebraic Topology does this using an indirect approach. Each geometric object is associated with a set of algebraic structures, usually groups . Questions about the geometric objects are converted into questions about the associated groups. This strategy is analogous to the way transform methods are used to solve differential equations. Laplace and Fourier transforms are used to convert a differential equation into a strictly algebraic equation. Algebraic methods are used to solve for the transform of the solution to the differential equation. The inverse transform is applied to the transform of the solution to get the solution to the differential equation. n Let X be a sphere in 3-space and let Y be a torus also in 3-space. The groups to be constructed are based upon loops that begin and end at some point P outside of X and Y. A loop is just a directed path in which the the beginning point and the end point are the same point. Two loops, x and x , can be added by attaching the beginning part of the second loop to the ending part of the first loop. There is also a zero loop, one that does not leave the point P. The situation is illustrated in the diagram below.

50. Research In Algebraic Topology
Geometry and algebraic topology play major roles throughout Mathematics and its applications, with geometric and topological ideas often being indispensable
http://www.maths.gla.ac.uk/research/groups/algebraic_topology/
Text only Department of Mathematics Home Research > Algebraic Topology Home Research Algebra Algebraic Topology ... Contact Algebraic Topology Geometry and Algebraic Topology play major roles throughout Mathematics and its applications, with geometric and topological ideas often being indispensable.
Algebraic Topology has developed important machinery such as cohomology theories including ordinary cohomology, K -theory, cobordism and elliptic cohomology.
These are often of use in geometric situations, as well as within Algebraic
Topology; Algebraic Topologists tend to study much less `rigid' geometric
situations than other Geometers.There have also been significant interactions with many areas of Algebra, and indeed much of Algebraic Topology can be viewed as `applied algebra' as well as being a major source of innovative algebraic ideas. In the words of Hermann Weyl: ` In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics Departmental research activity in Topology occurs in the following areas.

51. CAT04 - Arolla Conference On Algebrac Topology
CAT04. Arolla Conference on algebraic topology. August 24 through 29, 2004. Welcome to the main page of the CAT04 web site !
http://www2.unil.ch/cat04/

52. Short Course On Algebraic Topology, Gliwice, Poland, 3.9.2007
This (very) short course on algebraic topology shall give an introduction to some essenetial concepts of this field of mathematics the fundamental group
http://www.mathstat.helsinki.fi/~fluch/at_gliwice-07/
Department of Mathematics and Statistics
Faculty of Science

Faculty of Social Sciences

Departmental front page
News ... People In English
Short Course on Algebraic Topology
(Gliwice, Poland, 3.9.2007)
Lecturer
Martin Fluch
Content
This (very) short course on Algebraic Topology shall give an introduction to some essenetial concepts of this field of mathematics: the fundamental group and homology theories. As an example we will show how those results are used to prove that the Euclidean spaces R n and R m are not homeomorphic if n is not equal to m , which is not possible to prove in a purely topological way. This short lecture will be part of the 3rd Summer School of Algebra and Topology which is held in Gliwice , Poland from 3rd to 7th of September.
Lecture Notes
The notes to the lecture can be downloaded here: alg_top_intro.pdf
Literature
  • Fred Croom. Basic Concepts of Algebraic Topology . Undergraduate Texts in Mathematics. Springer-Verlag, 1978. Glen Bredon. Topology and Geometry . Graduate texts in mathematics. Springer-Verlag, 1993. Jean Dieudonne

53. FreeScience - Books - Algebraic Topology
This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in
http://www.freescience.info/books.php?id=102

54. Universität Osnabrück - Institut Für Mathematik - Conference On Algebraic Top
mailtoJP. Conference on algebraic topology. Osnabrück (Germany) Triangulated categories are fundamental tools in both algebra and topology.
http://www.mathematik.uni-osnabrueck.de/topRainer65.html
Direkt Zu Fachbereich Mathematik/Informatik AAA ZSB Stud.-Sekr. ... Adressen Interaktiv StudIP Webmail RZ Impressum/Kontakt Suche
Suche Mathematik
Aktuelles
Conference on Algebraic Topology Allgemeines
Vorstand
...
Local MathNet Guide

Conference on Algebraic Topology
Friday, October 12th, 2007
In honour of Prof. Dr. Rainer Vogt on his 65th birthday we take the opportunity to hold a conference.
Some impressions... Arrival building 69 first floor Zbigniew Fiedorowicz (Ohio) What is symmetric homology?
(joint with Shaun Ault)
We outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed simplicial groups and the homological algebra of module-valued functors. The symmetric homology of group algebras is related to stable homotopy theory. Two spectral sequences for computing symmetric homology are constructed. The relation to cyclic homology is discussed and a couple of conjectures towards further work are proposed. Clemens Berger (Nizza) The lattice path operad
We describe a coloured operad in sets permitting a uniform construction of several known combinatorial models of E n -operads. This is joint work with M.A. Batanin.

55. Mathematics :: Algebraic Topology --  Britannica Online Encyclopedia
Britannica online encyclopedia article on mathematics, algebraic topology The early 20th century saw the emergence of a number of theories whose power and
http://www.britannica.com/eb/article-66032/mathematics
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New! Britannica Book of the Year

56. Algebraic Topology From A Homotopical Viewpoint - EBook Download
The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications
http://download-ebook.org/index.php?target=desc&ebookid=145

57. Algebraic Topology
Superb 1year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.
http://store.doverpublications.com/0486691314.html
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58. Algebraic Topology
algebraic topology. Complex Analysis and Riemann Surfaces algebraic topology I I Homology Theory. Singular homology definition, simple computations
http://www.math.columbia.edu/crs/main/gradcourses/algtop.html
Search Email SSH FTP GENERAL INFORMATION ... RESEARCH COURSES PROGRAMS PEOPLE CALENDAR ALUMNI
Courses Overview All Courses Undergraduate Courses Graduate Core Courses ... Course and Exam Schedules
Graduate Core Courses Overview Analysis and Probability Modern Geometry Lie Groups and Representations Algebraic Topology Complex Analysis and Riemann Surfaces Algebraic Geometry and Number Theory Algebraic Topology Algebraic Topology I
I Homology Theory
  • Singular homology definition, simple computations Cellular homology definition Eilenberg-Steenrod Axioms for homology Computations: S n R P n C P n T n S S , Grassmannians, X*Y Alexander duality Jordan curve theorem and higher dimensional analogues Applications: Winding number, degree of maps, Brouwer fixed point theorem Lefschetz fixed point theorem
II Homotopy Theory
  • Homotopy of maps, of pointed maps The homotopy category and homotopy functors examples X x Van Kampen's theorem Higher homotopy groups and the Hurewicz theorem S Higher homotopy groups of the sphere
III Covering Spaces
  • Definition of a covering projection Examples Coverings of S S n covering R P n Spin n ) covering SO n Homotopy path lifting Classification of coverings of a reasonable space
IV Homology with Local Coefficients
  • Local coefficient systems Relation with covering spaces Obstruction theory The Alexander polynomial of a knot

Algebraic Topology II

I Cohomology
  • Cup products Pairings homology Cohomology and homology with coefficients Universal coefficient theorems

59. Science Central : Science - Math - Topology - Algebraic Topology
Category Listing Science Math - Topology - algebraic topology.
http://www.sciencecentral.com/category/26946
Friday, 14 March, 2008 Home Submit Science Site Add to Favorite Contact search for Directories Aeronautics and Aerospace Agriculture Anomalies and Alternative Science Astronomy ... Technology Category: Science Math Topology Algebraic Topology SUBMIT A SITE
Algebraic Topology Order by Popularity Alphabet Sites Records 1-17 of 17 Algebraic Topology Discussion List (Popularity:
Information on subscribing, archives of past discussions, and links to home pages of algebraic topologists.
Algebraic Topology and Concurrency
(Popularity:
Applications of algebraic topology to computer science.
Algebraic Topology
(Popularity:
In Dave Rusin's Mathematical Atlas.
Math Front: AT Algebraic Topology
(Popularity:
Preprints in algebraic topology.
Algebraic K-Theory, Linear Algebraic Groups and Related Structures
(Popularity:
TMR network coordinated in Bielefeld. Allen Hatcher's Homepage (Popularity: Contains textbooks in Algebraic Topology, K-Theory, and 3-Manifolds. Surgery Bits and Pieces (Popularity: Assembled by Andrew Ranicki. An Introduction to Algebraic K-theory (Popularity: A graduate textbook, some chapters online, by Charles Weibel.

60. Intute: Science, Engineering And Technology - Browse Algebraic Topology
Browse algebraic topology. Algebra algebraic topology at the University of Wales, Bangor. The research in algebra at Bangor concentrates on algebraic
http://www.intute.ac.uk/sciences/cgi-bin/browse.pl?id=25621

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