Combinatorial presentation of multidimensional persistent homology
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A multifiltration is a functor indexed by Nr that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural Nr-graded R[x1,…,xr]-module structure on the homology of a multifiltration of simplicial complexes. To do that we study multifiltrations of sets and vector spaces. We prove in particular that the Nr-graded R[x1,…,xr]-modules that can occur as R-spans of multifiltrations of sets are the direct sums of monomial ideals.
IdentifiersURN: urn:nbn:se:kth:diva-168007OAI: oai:DiVA.org:kth-168007DiVA: diva2:813837
QS 20152015-05-252015-05-252015-05-25Bibliographically approved