**Cloth**: 978-0-226-51178-8 |

**Electronic**: 978-0-226-51179-5

**DOI:**10.7208/chicago/9780226511795.001.0001

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**ABOUT THIS BOOK**

**AUTHOR BIOGRAPHY**

**REVIEWS**

**TABLE OF CONTENTS**

### ABOUT THIS BOOK

*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.

### AUTHOR BIOGRAPHY

**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 also in this series.

**K. Ponto**is assistant professor of mathematics at the University of Kentucky.

### REVIEWS

### TABLE OF CONTENTS

**Introduction**

**Some conventions and notations**

**Acknowledgments**

**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**

**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 p**

**24. A Primer on Spectral Sequences**

**Bibliography**

**Index**