Wolfgang Franz 
Algebraic Topology [PDF ebook] 

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