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Combinatorial presentation of multidimensional persistent homology
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2017 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 221, no 5, p. 1055-1075Article in journal (Refereed) Published
Abstract [en]

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 R-modules. 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.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 221, no 5, p. 1055-1075
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-200849DOI: 10.1016/j.jpaa.2016.09.001ISI: 000392783200002Scopus ID: 2-s2.0-85005784427OAI: oai:DiVA.org:kth-200849DiVA, id: diva2:1071208
Funder
Swedish Research Council, 2009-6102
Note

QC 20170203

Available from: 2017-02-03 Created: 2017-02-03 Last updated: 2017-11-29Bibliographically approved

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