Interleaving Mayer-Vietoris spectral sequences

Torras Casas, Álvaro ORCID: https://orcid.org/0000-0002-5099-6294 and Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 2024. Interleaving Mayer-Vietoris spectral sequences. Algebraic and Geometric Topology 24 (8) , pp. 4265-4306. 10.2140/agt.2024.24.4265

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Abstract

We discuss the Mayer–Vietoris spectral sequence as an invariant in the context of persistent homology. In particular, we introduce the notion of ε–acyclic carriers and ε–acyclic equivalences between filtered regular CW–complexes and study stability conditions for the associated spectral sequences. We also look at the Mayer–Vietoris blowup complex and the geometric realization, finding stability properties under compatible noise; as a result we prove a version of an approximate nerve theorem. Adapting work by Serre, we find conditions under which ε–interleavings exist between the spectral sequences associated to two different covers.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Mathematical Sciences Publishers (MSP)
ISSN:	1472-2747
Date of First Compliant Deposit:	23 May 2023
Date of Acceptance:	12 April 2023
Last Modified:	09 Jan 2025 11:22
URI:	https://orca.cardiff.ac.uk/id/eprint/159883

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