Author | Dold, Albrecht. author |
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Title | Lectures on Algebraic Topology [electronic resource] / by Albrecht Dold |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1972 |
Connect to | http://dx.doi.org/10.1007/978-3-662-00756-3 |
Descript | XI, 380 p. online resource |
I Preliminaries on Categories, Abelian Groups, and Homotopy -- ยง 1 Categories and Functors -- ยง 2 Abelian Groups (Exactness, Direct Sums, Free Abelian Groups) -- ยง 3 Homotopy -- II Homology of Complexes -- ยง 1 Complexes -- ยง 2 Connecting Homomorphism, Exact Homology Sequence -- ยง 3 Chain-Homotopy -- ยง 4 Free Complexes -- III Singular Homology -- ยง 1 Standard Simplices and Their Linear Maps -- ยง 2 The Singular Complex -- ยง 3 Singular Homology -- ยง 4 Special Cases -- ยง 5 Invariance under Homotopy -- ยง 6 Barycentric Subdivision -- ยง 7 Small Simplices. Excision -- ยง 8 Mayer-Vietoris Sequences -- IV Applications to Euclidean Space -- ยง 1 Standard Maps between Cells and Spheres -- ยง 2 Homology of Cells and Spheres -- ยง 3 Local Homology -- ยง 4 The Degree of a Map -- ยง 5 Local Degrees -- ยง 6 Homology Properties of Neighborhood Retracts in ?n -- ยง 7 Jordan Theorem, Invariance of Domain -- ยง 8 Euclidean Neighborhood Retracts (ENRs) -- V Cellular Decomposition and Cellular Homology -- ยง 1 Cellular Spaces -- ยง 2 CW-Spaces -- ยง 3 Examples -- ยง 4 Homology Properties of CW-Spaces -- ยง 5 The Euler-Poincarรฉ Characteristic -- ยง 6 Description of Cellular Chain Maps and of the Cellular Boundary Homomorphism -- ยง 7 Simplicial Spaces -- ยง 8 Simplicial Homology -- VI Functors of Complexes -- ยง 1 Modules -- ยง 2 Additive Functors -- ยง 3 Derived Functors -- ยง 4 Universal Coefficient Formula -- ยง 5 Tensor and Torsion Products -- ยง 6 Horn and Ext -- ยง 7 Singular Homology and Cohornology with General Coefficient Groups -- ยง 8 Tensorproduct and Bilinearity -- ยง 9 Tensorproduct of Complexes. Kรผnneth Formula -- ยง 10 Horn of Complexes.Homotopy Classification of Chain Maps -- ยง 11 Acyclic Models -- ยง 12 The Eilenberg-Zilber Theorem. Kรผnneth Formulas for Spaces -- VII Products -- ยง 1 The Scalar Product -- ยง 2 The Exterior Homology Product -- ยง 3 The Interior Homology Product (Pontrjagin Product) -- ยง 4 Intersection Numbers in ?n -- ยง 5 The Fixed Point Index -- ยง 6 The Lefschetz-Hopf Fixed Point Theorem -- ยง 7 The Exterior Cohomology Product -- ยง 8 The Interior Cohomology Product (?-Product) -- ยง 9 ?-Products in Projective Spaces. Hopf Maps and Hopf Invariant -- ยง 10 Hopf Algebras -- ยง 11 The Cohomology Slant Product -- ยง 12 The Cap-Product (?-Product) -- ยง 13 The Homology Slant Product, and the Pontrjagin Slant Product -- VIII Manifolds -- ยง 1 Elementary Properties of Manifolds -- ยง 2 The Orientation Bundle of a Manifold -- ยง 3 Homology of Dimensions ? n in n-Manifolds -- ยง 4 Fundamental Class and Degree -- ยง 5 Limits -- ยง 6 ?ech Cohomology of Locally Compact Subsets of ?n -- ยง 7 Poincarรฉ-Lefschetz Duality -- ยง 8 Examples, Applications -- ยง 9 Duality in ?-Manifolds -- ยง 10 Transfer -- ยง 11 Thom Class, Thom Isomorphism -- ยง 12 The Gysin Sequence. Examples -- ยง 13 Intersection of Homology Classes -- Appendix Kan- and ?ech-Extensions of Functors -- ยง 1 Limits of Functors -- ยง 2 Polyhedrons under a Space, and Partitions of Unity -- ยง 3 Extending Functors from Polyhedrons to More General Spaces