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About this book
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.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access More Concise Algebraic Topology by J. P. May,K. Ponto in PDF and/or ePUB format, as well as other popular books in Mathematics & Abstract Algebra. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Contents
- Introduction
- Some conventions and notations
- Acknowledgments
- Part 1: Preliminaries: Basic homotopytheory and nilpotent spaces
- Part 2: Localizations of spaces at sets of primes
- Part 3: Completions of spaces at sets of primes
- Part 4: An introduction to model category theory
- Part 5: Bialgebras and Hopf algebras
- Bibliography
- Index