Geodesic
Interleaving Mayer–Vietoris spectral sequences
Torras-Casas, Álvaro1 ; Pennig, Ulrich1
1 School of Mathematics, Cardiff University, Cardiff, United Kingdom
Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4265-4306

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2024.24.4265
Keywords: Mayer–Vietoris, acyclic carrier, interleaving, spectral sequence, regular morphism

Torras-Casas, Álvaro 1 ; Pennig, Ulrich 1

1 School of Mathematics, Cardiff University, Cardiff, United Kingdom 
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Torras-Casas, Álvaro; Pennig, Ulrich. Interleaving Mayer–Vietoris spectral sequences. Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4265-4306. doi: 10.2140/agt.2024.24.4265

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