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 systematic...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1991, 1991
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| Edition: | 1st ed. 1991 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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