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RELATIVE LERAY NUMBERS VIA SPECTRAL SEQUENCES
Author(s) -
Kalai Gil,
Meshulam Roy
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12103
Subject(s) - mathematics , vertex (graph theory) , combinatorics , simplicial complex , intersection (aeronautics) , lattice (music) , discrete mathematics , graph , physics , acoustics , engineering , aerospace engineering
Let F be a fixed field and let X be a simplicial complex on the vertex set V . The Leray number L ( X ; F ) is the minimal d such that for all i ⩾ d and S ⊂ V , the induced complex X [ S ] satisfiesH ∼ i ( X [ S ] ; F ) = 0 . Leray numbers play a role in formulating and proving topological Helly‐type theorems. For two complexes X , Y on the same vertex set V , define the relative Leray numberL Y ( X ; F )as the minimal d such thatH ∼ i ( X [ V ∖ τ ] ; F ) = 0 for all i ⩾ d and τ ∈ Y . In this paper we extend the topological colorful Helly theorem to the relative setting. Our main tool is a spectral sequence for the intersection of complexes indexed by a geometric lattice.