Description
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 Poincar Duality Theorem — Chapter 9. THE COHOMOLOGY RING OF A MANIFOLD — 30. Products in Manifolds — 31. Product Matrices — BIBLIOGRAPHY — INDEX
