Cover
Title page
Foreword
Chapter I Preliminaries on Categories, Abelian Groups, and Homotopy
1 Categories and Functors
2 Abelian Groups (Exactness, Direct Sums, Free Abelian Groups)
3 Homotopy
Chapter II Homology of Complexes
1 Complexes
2 Connecting Homomorphism, Exact Homology Sequence
3 Chain-Homotopy
4 Free Complexes
Chapter III Singular Homology
1 Standard Simplices and Their Linear Maps
2 The Singular Complex
3 Singular Homology
4 Special Cases
5 Invariance under Homotopy
6 Barycentric Subdivision
7 Small Simplices. Excision
8 Mayer-Vietoris Sequences
Chapter IV Applications to Euclidean Space
1 Standard Maps between Cells and Spheres
2 Homology of Cells and Spheres
3 Local Homology
4 The Degree of a Map
5 Local Degrees
6 Homology Properties of Neighborhood Retracts in R^n
7 Jordan Theorem, Invariance of Domain
8 Euclidean Neighborhood Retracts (ENRs)
Chapter V Cellular Decomposition and Cellular Homology
1 Cellular Spaces
2 CW-Spaces
3 Examples
4 Homology Properties of CW-Spaces
5 The Euler-PoincarΓ© Characteristic
6 Description of Cellular Chain Maps and of the Cellular Boundary Homomorphism
7 Simplicial Spaces
8 Simplicial Homology
Chapter VI Functors of Complexes
1 Modules
2 Additive Functors
3 Derived Functors
4 Univers al Coefficient Formula
5 Tensor and Torsion Products
6 Hom and Ext
7 Singular Homology and Cohomology with General Coefficient Groups
8 Tensorproduct and Bilinearity
9 Tensorproduct of Complexes. KΓΌnneth Formula
10 Hom of Complexes. Homotopy Classification of Chain Maps
11 Acyclic Models
12 The Eilenberg-Zilber Theorem. KΓΌnneth Formulas for Spaces
Chapter VII Products
1 The Scalar Product
2 The Exterior Homology Product
3 The Interior Homology Product (Pontrjagin Product)
4 Intersection Numbers in R^n
5 The Fixed Point Index
6 The Lefschetz-Hopf Fixed Point Theorem
7 The Exterior Cohomology Product
8 The Interior Cohomology Product (\cup-Product)
9 \cup-Products in Projective Spaces. Hopf Maps and Hopf Invariant
10 Hopf Algebras
11 The Cohomology Slant Product
12 The Cap-Product (\cap-Product)
13 The Homology Slant Product, and the Pontrjagin Slant Product
Chapter VIII Manifolds
1 Elementary Properties of Manifolds
2 The Orientation Bundle of a Manifold
3 Homology of Dimensions > n in n-Manifolds
4 Fundamental Class and Degree
5 Limits
6 Cech Cohomology of Locally Compact Subsets of R^n
7 PoincarΓ©-Lefschetz Duality
8 Examples, Applications
9 Duality in a-Manifolds
10 Transfer
11 Thom Class, Thom Isomorphism
12 The Gysin Sequence. Examples
13 Intersection of Homology Classes
Appendix Kan- and Cech-Extensions of Functors
1 Limits of Functors
2 Polyhedrons under a Space, and Partitions of Unity
3 Extending Functors from Polyhedrons to More General Spaces
Bibliography
Subject Index