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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

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

Extractions: 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 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/

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

Extractions: 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

Extractions: POINTERS: Texts Software Web links Selected topics here 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

Extractions: 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/

Extractions: 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 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 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

Extractions: 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

Extractions: 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

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

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

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

Extractions: Home Catalogue Google Book Search Search this book Library of Congress Record Textbook Cornell University, New York DOI: (Stock level updated: 14:22 GMT, 14 March 2008) â¢ Broad, readable coverage of the subject â¢ Geometric emphasis gives students better intuition â¢ Includes many examples and exercises ' â¦ 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 'â¦ clear and concise â¦ makes the book useful both as a basis for courses and as a reference work.' Monatshefte f¼r Mathematik 'â¦ the truly unusual abundance of instructive examples and complementing exercises is absolutely unique of such a kind â¦ 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/

Extractions: 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: 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/

Extractions: skip to content Home Courses Donate ... Mathematics Algebraic Topology II Pushout and pullback. (Image by MIT OCW.) This course features lecture notes and assignments 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. Instructor:

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

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/

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

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/

Extractions: 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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