Homology theory : an introduction to algebraic topology
著者
書誌事項
Homology theory : an introduction to algebraic topology
（Graduate texts in mathematics, 145）
Springer-Verlag, c1994
2nd ed
- : us
- : gw
- : softcover
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注記
First ed. published: New York : Academic Press, c1973. (Pure and applied mathematics ; v. 53)
Includes bibliographical references (p. 227-228), bibliography (p. 229-238), and index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387941264
内容説明
This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
目次
1 Singular Homology Theory.- 2 Attaching Spaces with Maps.- 3 The Eilenberg-Steenrod Axioms.- 4 Covering Spaces.- 5 Products.- 6 Manifolds and Poincare Duality.- 7 Fixed-Point Theory.- Appendix I.- Appendix II.- References.- Books and Historical Articles Since 1973.- Books and Notes.- Survey and Expository Articles.
- 巻冊次
-
: softcover ISBN 9781461269335
内容説明
This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
目次
1 Singular Homology Theory.- 2 Attaching Spaces with Maps.- 3 The Eilenberg-Steenrod Axioms.- 4 Covering Spaces.- 5 Products.- 6 Manifolds and Poincare Duality.- 7 Fixed-Point Theory.- Appendix I.- Appendix II.- References.- Books and Historical Articles Since 1973.- Books and Notes.- Survey and Expository Articles.
- 巻冊次
-
: gw ISBN 9783540941262
内容説明
This book is designed to be an introduction to some of the basic ideas in the field of algebraic topology. In particular, it is devoted to the foundations and applications of homology theory. The only prerequisite for the student is a basic knowledge of abelian groups and point set topology. The essentials of singular homology are given in the first chapter, along with some of the most important applications. In this way the student can quickly see the importance of the material. The successive topics include attaching spaces, finite CW complexes, the Eilenberg-Steenrod axioms, cohomology products, manifolds, Poincare duality, and fixed point theory. Throughout the book the approach is as illustrative as possible, with numerous examples and diagrams. Extremes of generality are sacrificed when they are likely to obscure the essential concepts involved. The book is intended to be easily read by students as a textbook for a course or as a source for individual study. The second edition has been substantially revised. It includes a new chapter on covering spaces in addition to illuminating new exercises.
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