In this chapter we associate to certain topological spaces a sequence of abelian groups, called homology groups, H r (K), for r = 0, 1, .... These groups give us information on the topological structure of K. For instance, H 0(K) measures the number of connected components of the space; the higher homology groups H r (K), for r > 0, intuitively speaking, measure the number of “r-dimensional holes” in K. A one-dimensional hole is a hole in the ordinary sense, a two-dimensional hole is an enclosed space, and so on.
KeywordsAbelian Group Topological Space Boundary Operator Simplicial Complex Homology Group
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