Interleaving Mayer-Vietoris spectral sequences
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910760086536192 |
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| author | Torras, Álvaro Pennig, Ulrich |
| author_facet | Torras, Álvaro Pennig, Ulrich |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_03307 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Interleaving Mayer-Vietoris spectral sequences Torras, Álvaro Pennig, Ulrich Algebraic Topology 55T, 18, 55N31 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. |
| title | Interleaving Mayer-Vietoris spectral sequences |
| topic | Algebraic Topology 55T, 18, 55N31 |
| url | https://arxiv.org/abs/2105.03307 |