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Introduction to Homotopy Theory

โœ Scribed by Paul S. Selick

Publisher
American Mathematical Society
Year
1997
Tongue
English
Leaves
212
Series
Fields Institute Monographs
Category
Library
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โœฆ Synopsis

This text is based on a one-semester graduate course taught by the author at The Fields Institute in fall 1995 as part of the homotopy theory program which constituted the Institute's major program that year. The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. The notes are divided into two parts: prerequisites and the course proper.
This book collects in one place the material that a researcher in algebraic topology must know. The author has attempted to make this text a self-contained exposition. Precise statements and proofs are given of "folk" theorems which are difficult to find or do not exist in the literature.

โœฆ Table of Contents

Cover
Title page
Dedication
Contents
Preface
Summary of global notation
Part I. Prerequisites
Prerequisites from category
Prerequisites from point set topology
The fundamental group
Homological algebra
Homology of spaces
Manifolds
Part II. Homotopy Theory
Higher homotopy theory
Simplicial sets
Fibre bundles and classifying spaces
Hopf algebras and graded Lie algebras
Spectral sequences
Localization and completion
Generalized homology and stable homotopy
Cohomology operations and the Steenrod algebra
Bibliography
Index
Back Cover

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