A Basic Course in Algebraic Topology
(Sprache: Englisch)
This textbook is intended 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...
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Klappentext zu „A Basic Course in Algebraic Topology “
This textbook is intended 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 unnecessary definitions, terminology, and technical machinery. 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 his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.
Inhaltsverzeichnis zu „A Basic Course in Algebraic Topology “
1: Two-Dimensional Manifolds2: The Fundamental Group
3: Free Groupsand Free Products of Groups
4: Seifert and Van Kampen Theorem on theFundamental 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: Determinationof the Homology Groups of Certain Spaces: Applications and FurtherProperties of Homology Theory
9: Homology of CW-Complexes
10:Homology with Arbitrary Coefficient Groups
11: The Homology ofProduct Spaces
12: Cohomology Theory
13: Products in Homology andCohomology
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: PermutationGroups or Tranformation Groups.
Autoren-Porträt von William S. Massey
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.
Bibliographische Angaben
- Autor: William S. Massey
- 1991, 1991, XVIII, 431 Seiten, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Herausgegeben: P. R. Halmos
- Verlag: Springer, Berlin
- ISBN-10: 038797430X
- ISBN-13: 9780387974309
- Erscheinungsdatum: 29.05.1997
Sprache:
Englisch
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