Homology Theory

An Introduction to Algebraic Topology

  • James W. Vick

Part of the Graduate Texts in Mathematics book series (GTM, volume 145)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. James W. Vick
    Pages 1-34
  3. James W. Vick
    Pages 35-64
  4. James W. Vick
    Pages 65-84
  5. James W. Vick
    Pages 85-119
  6. James W. Vick
    Pages 120-142
  7. James W. Vick
    Pages 143-185
  8. James W. Vick
    Pages 186-210
  9. Back Matter
    Pages 211-245

About this book


The 20 years since the publication of this book have been an era of continuing growth and development in the field of algebraic topology. New generations of young mathematicians have been trained, and classical problems have been solved, particularly through the application of geometry and knot theory. Diverse new resources for introductory coursework have appeared, but there is persistent interest in an intuitive treatment of the basic ideas. This second edition has been expanded through the addition of a chapter on covering spaces. By analysis of the lifting problem it introduces the funda­ mental group and explores its properties, including Van Kampen's Theorem and the relationship with the first homology group. It has been inserted after the third chapter since it uses some definitions and results included prior to that point. However, much of the material is directly accessible from the same background as Chapter 1, so there would be some flexibility in how these topics are integrated into a course. The Bibliography has been supplemented by the addition of selected books and historical articles that have appeared since 1973.


Algebraic topology CW complex cohomology fixed point theory homology point set topology set

Authors and affiliations

  • James W. Vick
    • 1
  1. 1.Department of MathematicsThe University of Texas at AustinAustinUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York Inc. 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6933-5
  • Online ISBN 978-1-4612-0881-5
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site