Singular Homology Theory
Seiten
2012
Springer-Verlag New York Inc.
978-1-4684-9233-0 (ISBN)
Springer-Verlag New York Inc.
978-1-4684-9233-0 (ISBN)
This textbook on homology and cohomology theory is geared towards the beginning graduate student. Singular homology theory is developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind various algebraic concepts is emphasized.
The only formal prerequisites are knowledge of the basic facts of abelian groups and point set topology. Singular Homology Theory is a continuation of t he author's earlier book, Algebraic Topology: An Introduction, which presents such important supplementary material as the theory of the fundamental group and a thorough discussion of 2-dimensional manifolds. However, this earlier book is not a prerequisite for understanding Singular Homology Theory.
The only formal prerequisites are knowledge of the basic facts of abelian groups and point set topology. Singular Homology Theory is a continuation of t he author's earlier book, Algebraic Topology: An Introduction, which presents such important supplementary material as the theory of the fundamental group and a thorough discussion of 2-dimensional manifolds. However, this earlier book is not a prerequisite for understanding Singular Homology Theory.
Chapter 1: Background and Motivation for Homology Theory.- Chapter 2: Definitions and Basic Properties of Homology Theory.- Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory.- Chapter 4: Homology of CW-complexes.- Chapter 5: Homology with Arbitrary Coefficient Groups.- Chapter 6: The Homology of Product Spaces.- Chapter 7: Cohomology Theory.- Chapter 8: Products in Homology and Cohomology.- Chapter 9: Duality Theorems for the Homology of Manifolds.- Chapter 10: Cup Products in Projective Spaces and Applications of Cup Products.- Appendix: A Proof of De Rham's Theorem.- Index.
| Reihe/Serie | Graduate Texts in Mathematics ; 70 |
|---|---|
| Zusatzinfo | XVI, 428 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-4684-9233-0 / 1468492330 |
| ISBN-13 | 978-1-4684-9233-0 / 9781468492330 |
| Zustand | Neuware |
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