More Concise Algebraic Topology

Localization, Completion, and Model Categories

J. P. May, K. Ponto

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English

University of Chicago Press
01 February 2012

Algebraic topology

Series: Chicago Lectures in Mathematics Series CLM

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.

By: J. P. May, K. Ponto
Imprint: University of Chicago Press
Country of Publication: United States
Dimensions: Height: 24mm, Width: 17mm, Spine: 4mm
Weight: 1.021kg
ISBN: 9780226511788
ISBN 10: 0226511782
Series: Chicago Lectures in Mathematics Series CLM
Pages: 544
Publication Date: 01 February 2012
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

J. Peter May is professor of mathematics at the University of Chicago and the author of several books, including A Concise Course in Algebraic Topology and Simplicial Objects in Algebraic Topology, both in the Chicago Lectures in Mathematics series. Kathleen Ponto is assistant professor of mathematics at the University of Kentucky.

Reviews for More Concise Algebraic Topology: Localization, Completion, and Model Categories

"""All researchers in algebraic topology should have at least a passing acquaintance with the material treated in this book, much of which does not appear in any of the standard texts."" (Kathryn Hess, Ecole Polytechnique Federale de Lausanne)"""