Wolfgang FranzAlgebraic Topology
Mitarbeit:Shore, Samuel D.;Übersetzung:Boron, Leo F.
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
