Homology Theory: An Introduction to Algebraic Topology
This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.
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Background to Part I
The Topology of Polyhedra
Homology Theory of a Simplicial Complex
The Contrahomology Ring for Polyhedra
Abelian Groups and Homological Algebra
The Fundamental Group and Covering Spaces
Autres éditions - Tout afficher
abelian group acyclic apply argument assertion associated boundary called chain complex chain homotopy chain map chapter clearly closed coefficients commutative compact condition connected consider consisting construct containing continuous contrachain contrahomology Corollary corresponding course covering cycle deduce define definition describe determines diagram dimension direct element equivalence exact sequence example exists extended face fact factor fibre filtration finite follows geometric give given hence homology groups homomorphism homotopy identify induces integer invariant isomorphism Moreover natural Notice observe obtain obvious operation ordered oriented pair path polyhedron projective proof Proposition prove reader regarded relation remark represents ring rule sequence simplex simplicial complex singular space structure subcomplex subgroup subset suppose Theorem theory topological unique vertex vertices write zero