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research article
Combinatorial presentation of multidimensional persistent homology
Chacholski, W.
•
Scolamiero, M.
•
Vaccarino, F.
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[x(1),...x(r)]-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[x(1),...,x(r)]-modules that can occur as R-spans of multifiltrations of sets are the direct sums of monomial ideals. (C) 2016 Elsevier B.V. All rights reserved.
Type
research article
Web of Science ID
WOS:000392783200002
Authors
Chacholski, W.
•
Scolamiero, M.
•
Vaccarino, F.
Publication date
2017
Publisher
Published in
Volume
221
Issue
5
Start page
1055
End page
1075
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
March 27, 2017
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