Contents
§10.7. Functoriality of homology
§10.8. Summary
Chapter 11. Homology of cell spaces
§11.1. Cellular complexes
§11.2. Example: homology of projective spaces
§11.3. Cell decomposition of Grassmann manifolds
Chapter 12. Morse theory
§12.1. Morse functions
§12.2. The cellular structure of a manifold endowed with
Morse function
§12.3. Attaching handles
§12.4. Regular Morse functions
§12.5. The boundary operator in a Morse complex
§12.6. Morse inequalities
§12.7. Standard bifurcations of Morse functions
Chapter 13. Cohomology and Poincare duality
§13.1. Cohomology
§13.2. Poincare duality for manifolds without boundary
§13.3. Manifolds with boundary and noncompact manifold
§13.4. Nonorientable manifolds
§13.5. Alexander duality
Chapter 14. Some applications of homology theory
§14.1. The Hopf invariant
§14.2. The degree of a map
§14.3. The total index of a vector field equals the Euler
characteristic
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