See also:

• Science: Math: Algebra  (395)
• Science: Math: Algebra: Category Theory  (40)

Allen Hatcher's Homepage:  .

- Links to online texts and papers (published and unpublished) on Algebraic Topology, K-Theory, and 3-Manifolds.

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. Brow.

Algebraic K-Theory, Linear Algebraic Groups and Related Structures: - TMR Network Project. Network Coordinator: Ulf Rehmann, Bielefel.

Algebraic Topology: - An encyclopedic reference containing definitions, some discussion, and an assortment of useful links to various resources concerning Algebraic Topology and K-Theory.

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.

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.

Algebraic Topology by Solomon Lefschetz: - Algebraic Topology text published by the American Mathematical Society (AMS), and available as a free download in PDF format.

Algebraic Topology Discussion List: - Includes information on subscribing, archives of past discussions, and links to home pages of algebraic topologists and other related resources.

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.




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.

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.

Ext Charts: - Charts for modules over the odd-primary Steenrod Algebra, by Christian Nassau. In Postscript.

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.

Higher Dimensional Group Theory: - This article by Prof. Ronald Brown discusses the advantageous application of groupoids to higher-dimensional Homotopy theory.

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.

The Hopf Fibration: - Notes and images of the Hopf map from S3 to S2.

Hopf Topology Archive: - A preprint archive of research papers on Algebraic Topology.

An Introduction to Algebraic K-theory: - An incomplete graduate textbook in Algebraic K-Theory, by Charles Weibel. Several chapters are available online.




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.

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

K-theory Preprint Archives: - An extensive archive of pre-publication papers (preprints) on Algebraic K-Theory.

Math Front: AT Algebraic Topology: - An archive of pre-publication papers (preprints) on Algebraic Topology.

MathWorld: - Index to more than 100 articles on Algebraic Topology.

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.

Open Problems in Algebraic Topology: - Problems in Algebraic Topology, compiled by mathematician Mark Hovey of Wesleyan University.

Poincaré Conjecture -- from MathWorld: - A widely accessible statement of the Poincaré Conjecture and its implications, with various links and references for further inquiry.

Surgery Bits and Pieces: - Assorted articles and minutia concerning Algebraic Surgery, assembled by Andrew Ranicki.




Table of the Homotopy Groups of Spheres: - From Toda's book: "Composition Methods in Homotopy Groups of Spheres.

What is Algebraic Topology?: - Introductory essay by Joe Neisendorfer, University of Rochester.