Introduction to Homotopy Theory

  • Martin Arkowitz

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Martin Arkowitz
    Pages 1-33
  3. Martin Arkowitz
    Pages 35-74
  4. Martin Arkowitz
    Pages 75-113
  5. Martin Arkowitz
    Pages 115-154
  6. Martin Arkowitz
    Pages 155-193
  7. Martin Arkowitz
    Pages 195-231
  8. Martin Arkowitz
    Pages 233-266
  9. Martin Arkowitz
    Pages 267-281
  10. Martin Arkowitz
    Pages 283-297
  11. Back Matter
    Pages 299-344

About this book

Introduction

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows:

• Basic homotopy;
• H-spaces and co-H-spaces;
• Fibrations and cofibrations;
• Exact sequences of homotopy sets, actions, and coactions;
• Homotopy pushouts and pullbacks;
• Classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead;
• Homotopy sets;
• Homotopy and homology decompositions of spaces and maps; and
• Obstruction theory.

The underlying theme of the entire book is the Eckmann-Hilton duality theory. This approach provides a unifying motif, clarifies many concepts, and reduces the amount of repetitious material. The subject matter is treated carefully with attention to detail, motivation is given for many results, there are several illustrations, and there are a large number of exercises of varying degrees of difficulty.

It is assumed that the reader has had some exposure to the rudiments of homology theory and fundamental group theory; these topics are discussed in the appendices. The book can be used as a text for the second semester of an algebraic topology course. The intended audience of this book is advanced undergraduate or graduate students. The book could also be used by anyone with a little background in topology who wishes to learn some homotopy theory.

Keywords

Eilenberg-Mac Lane and Moore spaces H-spaces and co-H-spaces fiber and cofiber spaces homotopy homotopy and homology decompositions homotopy groups loops and suspensions obstruction theory pushouts and pull backs universal coefficient theorems

Authors and affiliations

  • Martin Arkowitz
    • 1
  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7329-0
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7328-3
  • Online ISBN 978-1-4419-7329-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book