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SIMPLICIAL HOMOLOGY THEORY
The Barycentric Subdivision
29 other sections not shown
Abelian group acyclic carrier algebraic topology assume barycenter boundary called Cech homology theory cell complex chain complex chain cp chain homotopy chain map Chap closed cohomology compact pair consider construction continuous function convex CP(K CP(X CW complex cycle defined Definition denote diagram commutes dimension element epimorphism equation excision following diagram functor geometric complex Given group G hence homology groups homology sequence homology theory homomorphism Horn HP(K HP(X implies inclusion map integer inverse limit inverse system isomorphism Lemma 14 linear manifold map q Mayer-Vietoris sequence morphisms oriented pair map polyhedra polyhedron PROBLEMS Proof proper triad reader result satisfies Show simplex simplex sp simplicial approximation simplicial complex simplicial homology simplicial homology theory simplicial map singular homology subgroup subset subspace tion topological group topological pair topological space torus triangulation trivial unique vertices ZP(K