Simplicial Objects in Algebraic Topology

Simplicial Objects in Algebraic Topology

Simplicial sets are discrete analogs of topological spaces. They have played a central role in algebraic topology ever since their introduction in the late 1940s, and they also play an important role in other areas such as geometric topology and algebraic geometry. On a formal level, the homotopy theory of simplicial sets is equivalent to the homotopy theory of topological spaces. In view of this equivalence, one can apply discrete, algebraic techniques to perform basic topological constructions. These techniques are particularly appropriate in the theory of localization and completion of topological spaces, which was developed in the early 1970s. Since it was first published in 1967, Simplicial Objects in Algebraic Topology has been the standard reference for the theory of simplicial sets and their relationship to the homotopy theory of topological spaces. J. Peter May gives a lucid account of the basic homotopy theory of simplicial sets, together with the equivalence of homotopy theories alluded to above. The central theme is the simplicial approach to the theory of fibrations and bundles, and especially the algebraization of fibration and bundle theory in terms of "twisted Cartesian products." The Serre spectral sequence is described in terms of this algebraization. Other topics treated in detail include Eilenberg-MacLane complexes, Postnikov systems, simplicial groups, classifying complexes, simplicial Abelian groups, and acyclic models. "Simplicial Objects in Algebraic Topology presents much of the elementary material of algebraic topology from the semi-simplicial viewpoint. It should prove very valuable to anyone wishing to learn semi-simplicial topology. [May] has included detailed proofs, and he has succeeded very well in the task of organizing a large body of previously scattered material."—Mathematical Review

Download Now

Author
Publisher University of Chicago Press
Release Date
ISBN 0226511812
Pages 171 pages
Rating 4/5 (18 users)

More Books:

Simplicial Objects in Algebraic Topology
Language: en
Pages: 171
Authors: J. P. May
Categories: Mathematics
Type: BOOK - Published: 1992 - Publisher: University of Chicago Press

GET EBOOK

Simplicial sets are discrete analogs of topological spaces. They have played a central role in algebraic topology ever since their introduction in the late 1940
Simplicial Objects in Algebraic Topology
Language: en
Pages: 176
Authors: J. Peter May
Categories: Algebraic topology
Type: BOOK - Published: 1968 - Publisher:

GET EBOOK

A Concise Course in Algebraic Topology
Language: en
Pages: 262
Authors: J. P. May
Categories: Mathematics
Type: BOOK - Published: 1999-09 - Publisher: University of Chicago Press

GET EBOOK

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including
Handbook of Algebraic Topology
Language: en
Pages: 1324
Authors: I.M. James
Categories: Mathematics
Type: BOOK - Published: 1995-07-18 - Publisher: Elsevier

GET EBOOK

Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected
Algebraic Topology
Language: en
Pages: 462
Authors: Gunnar Carlsson
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer

GET EBOOK

These are proceedings of an International Conference on Algebraic Topology, held 28 July through 1 August, 1986, at Arcata, California. The conference served in
An Alpine Expedition through Algebraic Topology
Language: en
Pages: 296
Authors: Christian Ausoni
Categories: Mathematics
Type: BOOK - Published: 2014-06-09 - Publisher: American Mathematical Soc.

GET EBOOK

This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. Th
Effective Algebraic Topology
Language: en
Pages: 63
Authors: Rolf Schön
Categories: Mathematics
Type: BOOK - Published: 1991 - Publisher: American Mathematical Soc.

GET EBOOK

does not need QB copy
Adams Memorial Symposium on Algebraic Topology: Volume 1
Language: en
Pages: 320
Authors: Adams Memorial Symposium on Algebraic Topology (1990, Manchester)
Categories: Mathematics
Type: BOOK - Published: 1992-04-30 - Publisher: Cambridge University Press

GET EBOOK

Contains a combination of selected papers given in honour of John Frank Adams which illustrate the profound influence that he had on algebraic topology.
Combinatorial Algebraic Topology
Language: en
Pages: 416
Authors: Dimitry Kozlov
Categories: Mathematics
Type: BOOK - Published: 2008-01-08 - Publisher: Springer Science & Business Media

GET EBOOK

This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through t
Algebraic Topology
Language: en
Pages: 481
Authors: Martin C. Tangora
Categories: Mathematics
Type: BOOK - Published: 1993 - Publisher: American Mathematical Soc.

GET EBOOK

This book consists of twenty-nine articles contributed by participants of an International Conference in Algebraic Topology held in July 1991 in Oaxtepec, Mexic