A Basic Course in Algebraic Topology

William S. Massey

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English

Springer Verlag
01 June 1997

Mathematics & Sciences; Algebraic topology

Series: Graduate Texts in Mathematics

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.

By: William S. Massey
Imprint: Springer Verlag
Country of Publication: United States
Edition: 3rd
Volume: 127
Dimensions: Height: 235mm, Width: 155mm, Spine: 26mm
Weight: 1.780kg
ISBN: 9780387974309
ISBN 10: 038797430X
Series: Graduate Texts in Mathematics
Pages: 428
Publication Date: 01 June 1997
Audience: College/higher education , General/trade , Undergraduate , Further / Higher Education , ELT Advanced
Format: Hardback
Publisher's Status: Active

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 for A Basic Course in Algebraic Topology

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