A Basic Course in Algebraic Topology
Springer Berlin (Hersteller)
978-3-540-97430-7 (ISBN)
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This book is intended to serve as a textbook 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 unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized. 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 the now out-of- print SINGULAR HOMOLOGY THEORY (GTM 70). The material from the earlier books has been carefully revised, corrected, and brought up to date.
1: Two-Dimensional Manifolds. 2: 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.
| Reihe/Serie | Graduate Texts in Mathematics ; 127 |
|---|---|
| Zusatzinfo | 57 figs. in 91 parts |
| Sprache | deutsch |
| Gewicht | 764 g |
| Einbandart | gebunden |
| Schlagworte | Algebraische Topologie • HC/Mathematik/Arithmetik, Algebra • Topologie |
| ISBN-10 | 3-540-97430-X / 354097430X |
| ISBN-13 | 978-3-540-97430-7 / 9783540974307 |
| Zustand | Neuware |
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