RELATIVE LERAY NUMBERS VIA SPECTRAL SEQUENCES

Gil Kalai; Roy Meshulam

doi:10.1112/mtk.12103

RELATIVE LERAY NUMBERS VIA SPECTRAL SEQUENCES

Gil Kalai, Roy Meshulam^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let (Formula presented.) be a fixed field and let X be a simplicial complex on the vertex set V. The Leray number (Formula presented.) is the minimal d such that for all (Formula presented.) and (Formula presented.), the induced complex (Formula presented.) satisfies (Formula presented.). Leray numbers play a role in formulating and proving topological Helly-type theorems. For two complexes (Formula presented.) on the same vertex set V, define the relative Leray number (Formula presented.) as the minimal d such that (Formula presented.) for all (Formula presented.) and (Formula presented.). 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.

Original language	English
Pages (from-to)	730-737
Number of pages	8
Journal	Mathematika
Volume	67
Issue number	3
DOIs	https://doi.org/10.1112/mtk.12103
State	Published - Jul 2021

Bibliographical note

Publisher Copyright:
© 2021 The Authors. The publishing rights for this article are licensed to University College London under an exclusive licence.

Keywords

52A35
55U10

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10.1112/mtk.12103

Cite this

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RELATIVE LERAY NUMBERS VIA SPECTRAL SEQUENCES

Abstract

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Keywords

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