Combinatorial presentation of multidimensional persistent homology
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- 作者：W. Chachó ; lski<sup>asup><sup> ; sup><sup>1sup><sup> ; sup><sup>wojtek@math.kth.sesup> ; M. Scolamiero<sup>bsup><sup> ; sup><sup>martina.scolamiero@epfl.chsup> ; F. Vaccarino<sup>csup><sup> ; sup><sup>dsup><sup> ; sup><sup>2sup><sup> ; sup><sup>francesco.vaccarino@polito.itsup><sup> ; sup><sup>francesco.vaccarino@isi.itsup>
- 刊名：Journal of Pure and Applied Algebra
- 出版年：2017
- 出版时间：May 2017
- 年：2017
- 卷：221
- 期：5
- 页码：1055-1075
- 全文大小：541 K
- 卷排序：221
文摘
A multifiltration is a functor indexed by NrNr that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural NrNr-graded R[x1,…,xr]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 NrNr-graded R[x1,…,xr]R[x1,…,xr]-modules that can occur as R-spans of multifiltrations of sets are the direct sums of monomial ideals.