The Topology of CW Complexes
Springer-Verlag New York Inc.
978-1-4684-6256-2 (ISBN)
0. Preliminaries.- I. Combinatorial Cell Complexes.- 1. Definitions.- 2. Examples.- 3. Carrier theory.- 4. Functions.- 5. Product complexes.- 6. Equivalence relations and quotients.- 7. Adjunction complexes.- II. CW Complexes.- 1. Definitions.- 2. Alternative descriptions of CW complexes.- 3. Remarks on the general topology of CW complexes.- 4. Paracompactness.- 5. Products, quotients, and adjunctions.- 6. Homotopy and local properties.- 7. The homotopy extension theorem.- 8. The cellular approximation theorem.- 9. Aspherical carrier theorem.- III. Regular and Semisimplicial CW Complexes.- 1. Regular and normal CW complexes.- 2. Regular CW complexes and invariance of domain.- 3. Semisimplicial complexes.- 4. The realization of semisimplicial complexes.- 5. Semisimplicial constructions.- 6. Simplicial subdivision of semisimplicial complexes.- 7. Barycentric subdivision of semisimplicial complexes.- 8. Regulated semisimplicial complexes.- 9. The functor *.- IV. Homotopy Type of CW Complexes.- 1. Homotopy equivalence and deformation retraction.- 2. Homotopy equivalence of adjunction spaces.- 3. Whitehead’s theorems.- 4. Simplicial complexes with the metric topology.- 5. Equi-local convexity.- 6. Countable CW complexes.- 7. Finite CW complexes.- V. The Singular Homology of CW Complexes.- 1. Excision in the CW category.- 2. Cellular homology.- 3. Orientation, incidence, and degree.- 4. Regular CW complexes and proper maps.- 5. Quotient complexes.- 6. Product and adjunction complexes.- 7. Semisimplicial complexes.- 8. Realizing cellular maps.- Appendix I. Paracompact Spaces.- Appendix II. Extension Spaces and Neighborhood Retracts.
Erscheint lt. Verlag | 8.7.2012 |
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Reihe/Serie | The university series in higher mathematics |
Zusatzinfo | 10 Illustrations, black and white; VIII, 216 p. 10 illus. |
Verlagsort | New York, NY |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 1-4684-6256-3 / 1468462563 |
ISBN-13 | 978-1-4684-6256-2 / 9781468462562 |
Zustand | Neuware |
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