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Morse inequalities for the Koszul complex of multi-persistence
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- Guidolin, Andrea (author)
- KTH,SFW Matematik för Data och AI
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- Landi, Claudia (author)
- Univ Modena & Reggio Emilia, Reggio Emilia, Italy.
- (creator_code:org_t)
- Elsevier BV, 2023
- 2023
- English.
- In: Journal of Pure and Applied Algebra. - : Elsevier BV. - 0022-4049 .- 1873-1376. ; 227:7, s. 107319-
- Journal article (peer-reviewed)
Abstract
Subject headings
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- In this paper, we define the homological Morse numbers of a filtered cell complex in terms of relative homology of nested filtration pieces, and derive inequalities relating these numbers to the Betti tables of the multi-parameter persistence modules of the considered filtration. Using the Mayer-Vietoris spectral sequence we first obtain strong and weak Morse inequalities involving the above quantities, and then we improve the weak inequalities achieving a sharp lower bound for homological Morse numbers. Furthermore, we prove a sharp upper bound for homological Morse numbers, expressed again in terms of the Betti tables.
Subject headings
- NATURVETENSKAP -- Matematik -- Annan matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Other Mathematics (hsv//eng)
Keyword
- Persistence module
- Mayer-Vietoris spectral sequence
- Multigraded Betti numbers
- Euler characteristic
- Homological Morse numbers
Publication and Content Type
- ref (subject category)
- art (subject category)
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