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A Basic Course in Algebraic Topology

  • Textbook
  • © 1991

Overview

Authors:
  1. William S. Massey

    1. Department of Mathematics, Yale University, New Haven, USA

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  • Features topics such as the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory
  • Consists of material from the author's earlier titles, Algebraic Topology (GTM 56) and Singular Homology Theory (GTM 70)
  • Gives several applications of the methods of algebraic topology to concrete geometrical-topological problems

Part of the book series: Graduate Texts in Mathematics (GTM, volume 127)

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About this book

This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date. 

Keywords

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Two-Dimensional Manifolds

    • William S. Massey
    Pages 1-34

  3. The Fundamental Group

    • William S. Massey
    Pages 35-59

  4. Free Groups and Free Products of Groups

    • William S. Massey
    Pages 60-85

  5. Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications

    • William S. Massey
    Pages 86-116

  6. Covering Spaces

    • William S. Massey
    Pages 117-146

  7. Background and Motivation for Homology Theory

    • William S. Massey
    Pages 147-157

  8. Definitions and Basic Properties of Homology Theory

    • William S. Massey
    Pages 158-185

  9. Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory

    • William S. Massey
    Pages 186-224

  10. Homology of CW-Complexes

    • William S. Massey
    Pages 225-253

  11. Homology with Arbitrary Coefficient Groups

    • William S. Massey
    Pages 254-278

  12. The Homology of Product Spaces

    • William S. Massey
    Pages 279-304

  13. Cohomology Theory

    • William S. Massey
    Pages 305-322

  14. Products in Homology and Cohomology

    • William S. Massey
    Pages 323-349

  15. Duality Theorems for the Homology of Manifolds

    • William S. Massey
    Pages 350-393

  16. Cup Products in Projective Spaces and Applications of Cup Products

    • William S. Massey
    Pages 394-406

  17. Back Matter

    Pages 407-431
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Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    William S. Massey

About the author

William S. Massey (1920-2017) was an American mathematician known for his work in algebraic topology. The Blakers-Massey theorem and the Massey product were both named for him. His textbooks Singular Homology Theory and Algebraic Topology: An Introduction are also in the Graduate Texts in Mathematics series.

Bibliographic Information

  • Book Title: A Basic Course in Algebraic Topology

  • Authors: William S. Massey

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4939-9063-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 1991

  • Hardcover ISBN: 978-0-387-97430-9Published: 06 March 1991

  • eBook ISBN: 978-1-4939-9063-4Published: 28 June 2019

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XVIII, 431

  • Topics: Algebraic Geometry

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