Torras Casas, Álvaro ![]() ![]() ![]() |
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Official URL: https://doi.org/10.2140/agt.2024.24.4265
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 |
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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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