More concise algebraic topology : localization, completion, and model categories
 Author/Creator
 May, J. Peter.
 Language
 English.
 Imprint
 Chicago : University of Chicago Press, 2012.
 Physical description
 xxvii, 514 p. : ill. ; 24 cm.
 Series
 Chicago lectures in mathematics.
Access
Available online

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QA612 .M388 2012

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QA612 .M388 2012
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Contributors
 Contributor
 Ponto, Kate.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 497503) and index.
 Publisher's Summary
 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Algebraic topology.
Bibliographic information
 Publication date
 2012
 Responsibility
 J.P. May and K. Ponto.
 Series
 Chicago lectures in mathematics series
 ISBN
 9780226511788 (hardcover : alk. paper)
 0226511782 (hardcover : alk. paper)