Algebraic Topology

Algebraic K-theory, Groups and Categories
A report pursuant to the amalgamation in 1995 of two separate proposals for INTAS support in the areas of Algebraic K-theory, and Categorical Methods in Algebraic Homotopy and related topics. Period covered: 1997-2000. Project Coordinator: Prof. R. Brown
http://www.bangor.ac.uk/~mas010/intasrep.html

Algebraic K-Theory, Linear Algebraic Groups and Related Structures
TMR Network Project. Network Coordinator: Ulf Rehmann, Bielefeld
http://www.mathematik.uni-bielefeld.de/K+AG/

Algebraic Topology
An encyclopedic reference containing definitions, some discussion, and an assortment of useful links to various resources concerning Algebraic Topology and K-Theory.
http://en.wikipedia.org/wiki/Algebraic_topology

Algebraic Topology
Encyclopedic reference for "Algebraic Topology" in Dave Rusin's Mathematical Atlas. Includes a brief history along with various links to textbooks, reference works, and tutorials on the subject.
http://www.math.niu.edu/~rusin/known-math/index/55-XX.html

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

Algebraic Topology by Solomon Lefschetz
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/

Algebraic Topology Discussion List
Includes information on subscribing, archives of past discussions, and links to home pages of algebraic topologists and other related resources.
http://www.lehigh.edu/dmd1/public/www-data/algtop.html

Algebraic Topology Textbook
A complete, downloadable, introductory text on Algebraic Topology, by Prof. Allen Hatcher, Cornell Univ. 3rd Ed. 553 pp. with illustrations. Available in pdf and postscript versions.
http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Algorithms for the Fixed Point Property
A survey of various algorithms used to determine if a given ordered set has the fixed point property, that is, whether it has a fixed point free order-preserving self-map. Algorithms using the methods of Algebraic Topology are compared with other techniques.
http://www.csi.uottawa.ca/ordal/papers/schroder/FINSURVE.html

British Topology Home Page
A usable collection of pointers to Topology-related sites, including archives and conference announcements. The focus is mainly on British and European resources, with some links and references to research conducted in other parts of the globe.
http://www.maths.gla.ac.uk/~ajb/btop.phtml

Ext Charts
Charts for modules over the odd-primary Steenrod Algebra, by Christian Nassau. In Postscript.
http://www.nullhomotopie.de/charts/

Five talks on the Poincaré Conjecture
Streaming video links to lectures by Prof. John Morgan on the famous Poincaré Conjecture filmed during a 5-day series on the topic held at Columbia University on Monday, October 13, through Friday, October 17, 2003. Thurston Geometrization, and Hamilton’s ‘Ricci flow’ method, leading up to the Perelman’s proposed proof, are discussed. RealOne Player is required to view the video.
http://www.math.ohio-state.edu/lectures/clemens/five_talks.html

Higher Dimensional Group Theory
This article by Prof. Ronald Brown discusses the advantageous application of groupoids to higher-dimensional Homotopy theory.
http://www.bangor.ac.uk/~mas010/hdaweb2.htm

Homology, Homotopy and Applications - General Information
An all-electronic, peer-reviewed, international journal of leading-edge research in Homological and Homotopical Algebra, K-Theory, and applications.
http://www.math.rutgers.edu/hha/geninfo.html

The Hopf Fibration
Notes and images of the Hopf map from S3 to S2.
http://www.mathematik.uni-bielefeld.de/birep/top/hopf/hopf-fib.htm

Hopf Topology Archive
A preprint archive of research papers on Algebraic Topology.
ftp://hopf.math.purdue.edu/pub/hopf.html

An Introduction to Algebraic K-theory
An incomplete graduate textbook in Algebraic K-Theory, by Charles Weibel. Several chapters are available online.
http://www.math.rutgers.edu/~weibel/Kbook.html

K-theory
Encyclopedic reference for "K-Theory" in Dave Rusin's Mathematical Atlas. Includes a brief history along with various links to textbooks, reference works, and tutorials on the subject.
http://www.math.niu.edu/~rusin/known-math/index/19-XX.html

K-theory Calendar
A calendar of upcoming and past events (workshops, colloquia, lectures) pertaining to K-Theory and its applications.
http://www.math.uiuc.edu/K-theory/Calendar/

K-theory Preprint Archives
An extensive archive of pre-publication papers (preprints) on Algebraic K-Theory.
http://www.math.uiuc.edu/K-theory/

Math Front: AT Algebraic Topology
An archive of pre-publication papers (preprints) on Algebraic Topology.
http://front.math.ucdavis.edu/math.AT

MathWorld
Index to more than 100 articles on Algebraic Topology.
http://mathworld.wolfram.com/topics/AlgebraicTopology.html

Novikov Conjecture Home Page
An archive of developments concerning the Novikov Conjecture and related problems in Algebraic Topology, General Topology, Geometry, Algebra, and Analysis. Maintained by Jonathan Rosenberg.
http://www.math.umd.edu/users/jmr/NC.html

Open Problems in Algebraic Topology
Problems in Algebraic Topology, compiled by mathematician Mark Hovey of Wesleyan University.
http://claude.math.wesleyan.edu/~mhovey/problems/

Poincaré Conjecture -- from MathWorld
A widely accessible statement of the Poincaré Conjecture and its implications, with various links and references for further inquiry.
http://mathworld.wolfram.com/PoincareConjecture.html

Surgery Bits and Pieces
Assorted articles and minutia concerning Algebraic Surgery, assembled by Andrew Ranicki.
http://www.maths.ed.ac.uk/~aar/surgery/index.htm

Table of the Homotopy Groups of Spheres
From Toda's book: "Composition Methods in Homotopy Groups of Spheres."
http://www.math.nus.edu.sg/~matwujie/homotopy_groups_sphere.html

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