Overview

This book is intended to serve as a textbook 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 unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized. 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 the now out-of- print SINGULAR HOMOLOGY THEORY (GTM 70). The material from the earlier books has been carefully revised, corrected, and brought up to date.

Full Product Details

Author:   William S. Massey
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1st Corrected ed. 1991. Corr. 3rd printing 1997
Volume:   127
Dimensions:   Width: 15.50cm , Height: 2.60cm , Length: 23.50cm
Weight:   1.780kg
ISBN:  

9780387974309

ISBN 10:   038797430
Pages:   431
Publication Date:   06 March 1991
Audience:   College/higher education ,  General/trade ,  Postgraduate, Research & Scholarly ,  General
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1: Two-Dimensional Manifolds .- 2: The Fundamental Group .- 3: Free Groups and Free Products of Groups.-  4: Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications .-  5: Covering Spaces .- 6: Background and Motivation for Homology Theory .- 7: Definitions and Basic Properties of Homology Theory .- 8: Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory .- 9: Homology of CW-Complexes.-  10: Homology with Arbitrary Coefficient Groups .- 11: The Homology of Product Spaces.- 12: Cohomology Theory.- 13: Products in Homology and Cohomology.- 14: Duality Theorems for the Homology of Manifolds.- 15: Cup Products in Projective Spaces and Applications of Cup Products. Appendix A: A Proof of De Rham's Theorem..-  Appendix B: Permutation Groups or Tranformation Groups.

Reviews

W.S. MasseyA Basic Course in Algebraic Topology In the minds of many people algebraic topology is a subject which is esoteric, specialized, and disjoint from the overall sweep of mathematical thought. This straightforward introduction to the subject, by a recognized authority, aims to dispel that point of view by emphasizing: 1. the geometric motivation for the various concepts and 2. the applications to other areas. BULLETIN OF THE IRISH MATHEMATICS SOCIETY W.S. Massey A Basic Course in Algebraic Topology In the minds of many people algebraic topology is a subject which is a ~esoteric, specialized, and disjoint from the overall sweep of mathematical thought.a (TM) This straightforward introduction to the subject, by a recognized authority, aims to dispel that point of view by emphasizing: 1. the geometric motivation for the various concepts and 2. the applications to other areas. a BULLETIN OF THE IRISH MATHEMATICS SOCIETY

W.S. Massey <p>A Basic Course in Algebraic Topology <p> In the minds of many people algebraic topology is a subject which is a ~esoteric, specialized, and disjoint from the overall sweep of mathematical thought.a (TM) This straightforward introduction to the subject, by a recognized authority, aims to dispel that point of view by emphasizing: 1. the geometric motivation for the various concepts and 2. the applications to other areas. a BULLETIN OF THE IRISH MATHEMATICS SOCIETY

W.S. Massey A Basic Course in Algebraic Topology In the minds of many people algebraic topology is a subject which is a ~esoteric, specialized, and disjoint from the overall sweep of mathematical thought.a (TM) This straightforward introduction to the subject, by a recognized authority, aims to dispel that point of view by emphasizing: 1. the geometric motivation for the various concepts and 2. the applications to other areas. a BULLETIN OF THE IRISH MATHEMATICS SOCIETY

Author Information

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.

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