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List 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
