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Singular Homology Theory

  • Textbook
  • © 1980

Overview

Authors:
  1. William S. Massey

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

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 70)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. Background and Motivation for Homology Theory

    • William S. Massey
    Pages 1-10

  3. Definitions and Basic Properties of Homology Theory

    • William S. Massey
    Pages 11-37

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

    • William S. Massey
    Pages 38-75

  5. Homology of CW-complexes

    • William S. Massey
    Pages 76-104

  6. Homology with Arbitrary Coefficient Groups

    • William S. Massey
    Pages 105-128

  7. The Homology of Product Spaces

    • William S. Massey
    Pages 129-153

  8. Cohomology Theory

    • William S. Massey
    Pages 154-171

  9. Products in Homology and Cohomology

    • William S. Massey
    Pages 172-198

  10. Duality Theorems for the Homology of Manifolds

    • William S. Massey
    Pages 199-238

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

    • William S. Massey
    Pages 239-250

  12. Back Matter

    Pages 251-267
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Keywords

About this book

This textbook on homology and cohomology theory is geared towards the beginning graduate student. Singular homology theory is developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind various algebraic concepts is emphasized.

The only formal prerequisites are knowledge of the basic facts of abelian groups and point set topology. Singular Homology Theory is a continuation of t he author's earlier book, Algebraic Topology: An Introduction, which presents such important supplementary material as the theory of the fundamental group and a thorough discussion of 2-dimensional manifolds. However, this earlier book is not a prerequisite for understanding Singular Homology Theory. 

Authors and Affiliations

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

    William S. Massey

Bibliographic Information

  • Book Title: Singular Homology Theory

  • Authors: William S. Massey

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9231-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1980

  • Softcover ISBN: 978-1-4684-9233-0Published: 01 August 2012

  • eBook ISBN: 978-1-4684-9231-6Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XVI, 428

  • Topics: Algebraic Geometry

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