We turn now to the problem of comparing polyhedra by means of their associated homology groups. Comparisons between two topological spaces are usually made on the basis of a continuous map, ideally a homeomorphism, from one space to another. Groups are compared by means of homomor-phisms and isomorphisms. We shall show in this chapter that a continuous map f: |K| → |L| induces for each non-negative integer p a homomorphism f* p : H P (K) → H P (L) on the associated homology groups. This will allow topological comparisons between the polyhedra |K| and |L| on the basis of algebraic similarities between their associated homology groups.
KeywordsVector Field Topological Space Simplicial Approximation Homology Group Chain Mapping
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