Spectra and the Steenrod Algebra :Modules over the Steenrod Algebra and the Stable Homotopy Category ( North-Holland Mathematical Library )

Publication subTitle :Modules over the Steenrod Algebra and the Stable Homotopy Category

Publication series :North-Holland Mathematical Library

Author: Margolis   H. R.  

Publisher: Elsevier Science‎

Publication year: 2011

E-ISBN: 9780080960173

P-ISBN(Paperback): 9780444865168

P-ISBN(Hardback):  9780444865168

Subject: O189.23 homotopy theory

Language: ENG

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Description

I have intended this book to be more than just the sum of its chapters, and the introduction is, in part, an attempt to spell out what the more is. Algebraic topology is the study of topological problems by algebraic means. More precisely, this has come to be framed as the study of topological categories by means of functors to algebraic categories. Beyond the basic definitions and structure, the focus is often on particular problems, for example, Adams’ use of K-theory to solve the vector fields on spheres problem. On the other hand, there are contributions of a more global nature yielding insight into the overall structure of some topological category, for example, Quillen’s work on rational homotopy type. This book is intended primarily as a contribution of this latter sort. So while there will be a variety of particular examples and computations, and although the structure being developed has significant application to many specific problems (some of which are considered here), the major thrust of the text is toward understanding the global structure and linkage of the topological and algebraic categories considered: the stable homotopy category and the category of modules over the Steenrod algebra.

Chapter

Front Cover

pp.:  1 – 4

Copyright Page

pp.:  5 – 17

Introduction

pp.:  6 – 22

Contents

pp.:  17 – 6

Part II: The Steenrod Algebra and Spectra: Surface Structure

pp.:  188 – 332

Part III: The Steenrod Algebra and Spectra: Deep Structure

pp.:  332 – 460

Appendices

pp.:  460 – 501

Bibliography

pp.:  501 – 506

Symbol List

pp.:  506 – 508

Index

pp.:  508 – 512

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