Simplicial Objects in Algebraic Topology

J. P. May

ISBN 10: 0226511812 / ISBN 13: 9780226511818

Published by The University of Chicago Press, 1993

About this Item

Series: Chicago Lectures in Mathematics. Num Pages: 170 pages, black & white illustrations. BIC Classification: PBPD. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 142 x 218 x 15. Weight in Grams: 246. . 1993. Paperback. . . . . Books ship from the US and Ireland.

Seller Inventory # V9780226511818

Bibliographic Details

• Title: Simplicial Objects in Algebraic Topology
• Publisher: The University of Chicago Press
• Publication Date: 1993
• Language: English
• ISBN 10: 0226511812
• ISBN 13: 9780226511818
• Binding: Soft cover
• Edition: 2nd Edition
• Condition: New

About this title

Synopsis

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

About the Author

J. P. May is professor of mathematics at the University of Chicago; he is the author or coauthor of many papers and books, including Simplicial Objects in Algebraic Topology and A Concise Course in Algebraic Topology, both in the Chicago Lectures in Mathematics series.