More Concise Algebraic Topology: Localization, Completion, and Model Categories (Chicago Lectures in Mathematics Series) May, J. Peter and Kathleen Ponto

May, J. Peter and Kathleen Ponto

ISBN 10: 0226511782 / ISBN 13: 9780226511788

Published by The University of Chicago Press., 2012

About this Item

More Concise Algebraic Topology: Localization, Completion, and Model Categories (Chicago Lectures in Mathematics Series) In englischer Sprache. pages.

Seller Inventory # BN475355

Bibliographic Details

• Title: More Concise Algebraic Topology: Localization, Completion, and Model Categories (Chicago Lectures in Mathematics Series) May, J. Peter and Kathleen Ponto
• Publisher: The University of Chicago Press.
• Publication Date: 2012
• Language: English
• ISBN 10: 0226511782
• ISBN 13: 9780226511788
• Binding: Hardcover
• Edition: 2012.
• Condition: gut
• Weight: 2000 grams

About this title

Synopsis

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.

About the Authors

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. 

Kathleen Ponto is assistant professor of mathematics at the University of Kentucky.