Singular and Simplicial Homology Groups
Keywords:Boundary operator, Simplicial complex, Singular homology
This paper identified the homology groups of -simplex, -dimensional simplicial complex and -complex. We show that a -simplex is a point or a vertex, -simplex is a line or an edge, a -simplex is defined to be a triangle with its interior included and a -simplex is a solid tetrahedron. It is easy to continue to any -simplex . The aims of this paper are to construct and defined Singular Homology Groups and Simplicial Homology Groups in terms of -dimensional simplicial complex and a topological space . We followed the historical analysis mathematical method. We found that simplexes are building blocks of polyhedron, both approaches yield the same results, and the homology groups are quotient groups of -cycle groups and -boundary groups .
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