An Introduction to Algebraic Topology |
Contents
THE HOMOLOGY GROUPS OF A COMPLEX | 11 |
THE HOMOLOGY GROUPS OF A POLYTOPE | 47 |
ELEMENTARY APPLICATIONS | 95 |
Copyright | |
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Common terms and phrases
a₁ a₂ algebraic topology antipodal points assigns barycentric coordinates barycentric subdivision boundary c₁ called chain complex chain homotopy chain transformation closure coefficient group commutative completes the proof contained contiguity class continuous function covariant functor cycle defined definition degree denoted diagram dimension element elementary integral r-chain equation Euclidean example EXERCISE exists fixed-point property follows function f given graded group graded homology group group G h₁ h₂ Hom(X homology groups homology theory homomorphism hyperplane identity map induced homomorphism integer isomorphic K₁ K₂ L₁ L₂ Lemma linear map f map ƒ morphism n-simplexes nullhomotopic oriented simplex polytope map polytope pair proof of Theorem Prove Theorem r-dimensional chains respect sequence Show simplicial approximation simplicial map simplicial pair star related subcomplex symbol Theorem 11 Theorem 20 topological pairs topological spaces tr(t triangulation v₁ vector distribution vector space vertex winding number zero α₁