More Concise Algebraic Topology : Localization, Completion, and Model Categories

J. P. May
Bok · Engelsk · 2011 · Electronic books.

Annen tittel	Chicago Lectures in Mathematics
Medvirkende	Ponto, Kate.
Utgitt	Chicago, IL : : University of Chicago Press, , 2011.
Omfang	1 online resource (544 p.)
Opplysninger	Description based upon print version of record.. - 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 primes10. 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 algebras20. 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. - 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 topologist
Emner	Algebra. Algebraic topology. Algebraisk topologi Assosiative algebraer Vis mer... Geometry Homotopiteori Hopf-algebraer Komplettering Lokalisering Mathematics Modellkategorier Physical Sciences & Mathematics algebraisk topologi homotopi kategorier kategoriteori algebra
Sjanger	Electronic books.
Dewey	514.2
ISBN	0226511782. - 9780226511788