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Singular and Simplicial Homology
Chain ComplexesHomology and Cohomology
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algebraic homotopy inverse boundary operator called Cech homology groups cell decomposition chain complex chain groups chain homomorphism coboundary cochain cocycle coefficient group cofinal cohomology class cohomology ring constructed contained continuous map coordinates corresponding defined Definition denoted dimension direct sum dual element example excision theorem Exercise finite open covering following diagram formula geometric Hence homo homology sequence homology theory homomor homotopy theorem HP(E Hp(K identity map implies inclusion map induced homomorphisms integers intersection inverse limit inverse system isomorphism kernel Lemma linear map morphism notation Note nxfi obtained open set oriented cell oriented simplexes oriented simplicial pair of spaces path phism Proof proved quotient group relation represented respectively result satisfied shown simplicial chain simplicial complex simplicial homology simplicial map simplicial pair singular chain singular homology singular simplex subcomplex subset subspace system of homomorphisms topological space triangulable zero