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

By May, J. P.; Ponto, K.

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Book Id: WPLBN0003761149
Format Type: PDF eBook :
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Reproduction Date: 2015

Title: More Concise Algebraic Topology Localization, Completion, and Model Categories II  
Author: May, J. P.; Ponto, K.
Volume:
Language: English
Subject: Programming, Mathematics, Topology
Collections: Technical eBooks and Manuals Collection, Technical Books Center Collection
Historic
Publication Date:
2010
Publisher: Technical Books Center

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May, J. P., & Ponto, K. (2010). More Concise Algebraic Topology Localization, Completion, and Model Categories II. Retrieved from http://self.gutenberg.org/


Description
Description: This book explains the following topics: the fundamental group, covering spaces, ordinary homology and cohomology in its singular, cellular, axiomatic, and represented versions, higher homotopy groups and the Hurewicz theorem, basic homotopy theory including fibrations and cofibrations, Poincare duality for manifolds and manifolds with boundary.

Table of Contents
TOC: Preliminaries: basic homotopy theory and nilpotent spaces - Cofibrations and fibrations - Homotopy colimits and homotopy limits; lim1 - Nilpotent spaces and Postnikov towers - Detecting nilpotent groups and spaces - Localizations of spaces at sets of primes - Localizations of nilpotent groups and spaces - Characterizations and properties of localizations - Fracture theorems for localization: groups - Fracture theorems for localization: spaces - Rational H-spaces and fracture theorems - Completions of spaces at sets of primes - Completions of nilpotent groups and spaces - Characterizations and properties of completions - Fracture theorems for completion: Groups - Fracture theorems for completion: Spaces - An introduction to model category theory - An introduction to model category theory - Cofibrantly generated and proper model categories - Categorical perspectives on model categories - Model structures on the category of spaces - Model structures on categories of chain complexes - Resolution and localization model structures - Bialgebras and Hopf algebras - Bialgebras and Hopf algebras - Connected and component Hopf algebras - Lie algebras and Hopf algebras in characteristic zero - Restricted Lie algebras and Hopf algebras in characteristic p - A primer on spectral sequences.

 

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