Springer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of the Second Edition.
Inhaltsverzeichnis
I Preliminaries on Categories, Abelian Groups, and Homotopy. - §1 Categories and Functors. - §2 Abelian Groups (Exactness, Direct Sums, Free Abelian Groups). - §3 Homotopy. - II Homology of Complexes. - §1 Complexes. - §2 Connecting Homomorphism, Exact Homology Sequence. - §3 Chain-Homotopy. - §4 Free Complexes. - 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. - 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 ? n. - §7 Jordan Theorem, Invariance of Domain. - §8 Euclidean Neighborhood Retracts (ENRs). - V Cellular Decomposition and Cellular Homology. - §1 Cellular Spaces. - §2 CW-Spaces. - §3 Examples. - §4 HomologyProperties of CW-Spaces. - §5 The Euler-Poincaré Characteristic. - §6 Description of Cellular Chain Maps and of the Cellular Boundary Homomorphism. - §7 Simplicial Spaces. - §8 Simplicial Homology. - VI Functors of Complexes. - §1 Modules. - §2 Additive Functors. - §3 Derived Functors. - §4 Universal Coefficient Formula. - §5 Tensor and Torsion Products. - §6 Horn and Ext. - §7 Singular Homology and Cohomology with General Coefficient Groups. - §8 Tensorproduct and Bilinearity. - §9 Tensorproduct of Complexes. Künneth Formula. - §10 Horn of Complexes. Homotopy Classification of Chain Maps. - §11 Acyclic Models. - §12 The Eilenberg-Zilber Theorem. Kunneth Formulas for Spaces. - VII Products. - §1 The Scalar Product. - §2 The Exterior Homology Product. - § 3 The Interior Homology Product (Pontijagin Product). - § 4 Intersection Numbers in ? n. - §5 The Fixed Point Index. - §6 The Lefschetz-Hopf Fixed Point Theorem. - §7 The Exterior Cohomology Product. - § 8 The Interior Cohomology Product (? -Product). - § 9 ? -Products in Projective Spaces. Hopf Maps and Hopf Invariant. - §10 Hopf Algebras. - §11 The Cohomology Slant Product. - §12 The Cap-Product (? -Product). - § 13 The Homology Slant Product, and the Pontijagin Slant Product. - 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 ? ech Cohomology of Locally Compact Subsets of ? n. - §7 Poincaré-Lefschetz Duality. - §8 Examples, Applications. - §9 Duality in ? -Manifolds. - §10 Transfer. - §11 Thom Class, Thom Isomorphism. - §12 The Gysin Sequence. Examples. - §13 Intersection of Homology Classes. - Appendix: Kan- and ? ech-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.
