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arXiv · 2105.03307

Interleaving Mayer-Vietoris spectral sequences

Álvaro Torras·Ulrich Pennig
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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 $\varepsilon$-acyclic carriers and $\varepsilon$-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 $\varepsilon$-interleavings exist between the spectral sequences associated to two different covers.

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Álvaro Torras, Ulrich Pennig. 2021-05-07. Interleaving Mayer-Vietoris spectral sequences. https://doi.org/10.2140/agt.2024.24.4265

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