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