M ay 2 01 2 Annotating Simplices with a Homology Basis and Its Applicatons ∗

Abstract

Let K be a simplicial complex and g the rank of its p-th homology group Hp(K) defined with Z2 coefficients. We show that we can compute a basis H of Hp(K) and annotate each p-simplex of K with a binary vector of length g with the following property: the annotations, summed over all p-simplices in any p-cycle z, provide the coordinate vector of the homology… (More)

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