More Concise Algebraic Topology Localization Completion and Model Categories 1st Edition by J P May, K Ponto ISBN 0226511782 9780226511788

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ISBN 10: 0226511782 
ISBN 13: 9780226511788
Author: J P  May, K Ponto

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.

More Concise Algebraic Topology Localization Completion and Model Categories 1st Edition Table of contents:

Part 1: Preliminaries: Basic homotopytheory and nilpotent spaces

1. Cofibrations and Fibrations

2. Homotopy Colimits and Homotopy Limits; lim1

3. Nilpotent Spaces and Postnikov Towers

4. Detecting Nilpotent Groups and Spaces

Part 2: Localizations of spaces at sets of primes

5. Localizations of Nilpotent Groups and Spaces

6. Characterizations and Properties of Localizations

7. Fracture Theorems for Localization: Groups

8. Fracture Theorems for Localization: Spaces

9. Rational H-Spaces and Fracture Theorems

Part 3: Completions of spaces at sets of primes

10. Completions of Nilpotent Groups and Spaces

11. Characterizations and Properties of Completions

12. Fracture Theorems for Completion: Groups

13. Fracture Theorems for Completion: Spaces

Part 4: An introduction to model category theory

14. An Introduction to Model Category Theory

15. Cofibrantly Generated and Proper Model Categories

16. Categorical Perspectives on Model Categories

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