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**About this book :- **
**More Concise Algebraic Topology ** written by
** J. P. May, K. Ponto **.

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.
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.

**Book Detail :- **
** Title: ** More Concise Algebraic Topology
** Edition: **
** Author(s): ** J. P. May, K. Ponto
** Publisher: **
** Series: **
** Year: **
** Pages: ** 404
** Type: ** PDF
** Language: ** English
** ISBN: ** 0226511782, 978-0226511788
** Country: ** US
** Get this book from Amazon**

**About Author :- **

** 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.

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The author ** • Download PDF Basic Algebraic Topology and its Applications by Mahima Adhikari **

The author ** • Download PDF A Concise Course in Algebraic Topology by J. P. May **

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**Book Contents :- **
**More Concise Algebraic Topology ** written by
** J. P. May, K. Ponto **
cover the following topics.
****Part-1 Preliminaries: Basic homotopy theory 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

17. Model structures on the category of spaces

18. Model structures on categories of chain complexes

19. Resolution and localization model structures
****Part-5 Bialgebras and Hopf algebras**

20. Bialgebras and Hopf algebras

21. Connected and component Hopf algebras

22. Lie algebras and Hopf algebras in characteristic zero

23. Restricted Lie algebras and Hopf algebras in characteristic

24. A primer on spectral sequences

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