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Mathematics - Geometry & Topology | Homology Theory - An Introduction to Algebraic Topology

Homology Theory

An Introduction to Algebraic Topology

Series: Graduate Texts in Mathematics, Vol. 145

Vick, James W.

Originally published by Academic Press, New York, 1973

2nd ed. 1994, XIV, 245 p.

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  • About this textbook

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.

Content Level » Graduate

Keywords » Algebraic topology - CW complex - cohomology - fixed point theory - homology - point set topology - set

Related subjects » Geometry & Topology

Table of contents 

1 Singular Homology Theory.- 2 Attaching Spaces with Maps.- 3 The Eilenberg-Steenrod Axioms.- 4 Covering Spaces.- 5 Products.- 6 Manifolds and Poincaré Duality.- 7 Fixed-Point Theory.- Appendix I.- Appendix II.- References.- Books and Historical Articles Since 1973.- Books and Notes.- Survey and Expository Articles.

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