Algebraic Topology / / Wolfgang Franz.
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| Superior document: | Title is part of eBook package: De Gruyter DGBA Mathematics - <1990 |
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| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2020] ©1968 |
| Year of Publication: | 2020 |
| Edition: | Translated from the German original “Topologie II: Algebraische Topologie”. Reprint 2020 |
| Language: | English |
| Online Access: | |
| Physical Description: | 1 online resource (V, 170 p.) |
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Table of Contents:
- Frontmatter
- CONTENTS
- INTRODUCTION
- § 1. Analytic and Algebraic Topology
- § 2. Problems and Examples
- PART I. SIMPLICIAL COMPLEXES
- Chapter 1. GEOMETRY OF SIMPLICIAL COMPLEXES
- § 3. Hulls and Stars
- § 4. Barycentric Stars
- § 5. Simplicial Mappings
- § 6. Neighboring Mappings
- Chapter 2. HOMOLOGY GROUPS AND COHOMOLOGY GROUPS
- § 7. Orientation. Incidence Numbers
- § 8. Homology Groups
- § 9. Examples and Applications
- § 10. Cohomology Groups
- § 11. Homotopic Mappings
- PART II. CHAIN COMPLEXES AND THEIR APPLICATIONS
- Chapter 3. GENERAL THEORY
- § 12. Homology Groups of Chain Complexes
- § 13. Subcomplexes and Factor Complexes
- § 14. The Boundary Operator
- Chapter 4. FREE CHAIN COMPLEXES
- § 15. Modules and Dual Modules
- § 16. Mappings and Dual Mappings
- § 17. Free Chain Complexes. Canonical Bases
- PART III. CELL COMPLEXES. INVARIANCE
- Chapter 5. CELL COMPLEXES
- § 18. Cell Decompositions
- § 19. The Homology Groups of Cell Decompositions
- § 20. Normal Subdivisions
- Chapter 6. INVARIANCE OF THE HOMOLOGY GROUPS
- § 21. Proof of Invariance
- § 22. Supplements. Generalizations
- § 23. Results and Applications
- § 24. Local Homology Groups
- PART IV. DEVELOPMENT OF THE THEORY
- Chapter 7. PRODUCTS IN POLYHEDRA
- § 25. The Cohomology Ring
- § 26. The Cap Product
- Chapter 8. MANIFOLDS
- § 27. Definitions
- § 28. Complementary Cell Decompositions
- § 29. The Poincaré Duality Theorem
- Chapter 9. THE COHOMOLOGY RING OF A MANIFOLD
- § 30. Products in Manifolds
- § 31. Product Matrices
- BIBLIOGRAPHY
- INDEX