K-Theory of Multi-parameter Persistence Modules: Additivity
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916495386214400 |
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| author | Grady, Ryan E. Schenfisch, Anna |
| author_facet | Grady, Ryan E. Schenfisch, Anna |
| contents | Persistence modules stratify their underlying parameter space, a quality that make persistence modules amenable to study via invariants of stratified spaces. In this article, we extend a result previously known only for one-parameter persistence modules to grid multi-parameter persistence modules. Namely, we show the $K$-theory of grid multi-parameter persistence modules is additive over strata. This is true for both standard monotone multi-parameter persistence as well as multi-parameter notions of zig-zag persistence. We compare our calculations for the specific group $K_0$ with the recent work of Botnan, Oppermann, and Oudot, highlighting and explaining the differences between our results through an explicit projection map between computed groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06540 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | K-Theory of Multi-parameter Persistence Modules: Additivity Grady, Ryan E. Schenfisch, Anna Algebraic Topology Computational Geometry Category Theory K-Theory and Homology 18F25, 55N31, 19M05 Persistence modules stratify their underlying parameter space, a quality that make persistence modules amenable to study via invariants of stratified spaces. In this article, we extend a result previously known only for one-parameter persistence modules to grid multi-parameter persistence modules. Namely, we show the $K$-theory of grid multi-parameter persistence modules is additive over strata. This is true for both standard monotone multi-parameter persistence as well as multi-parameter notions of zig-zag persistence. We compare our calculations for the specific group $K_0$ with the recent work of Botnan, Oppermann, and Oudot, highlighting and explaining the differences between our results through an explicit projection map between computed groups. |
| title | K-Theory of Multi-parameter Persistence Modules: Additivity |
| topic | Algebraic Topology Computational Geometry Category Theory K-Theory and Homology 18F25, 55N31, 19M05 |
| url | https://arxiv.org/abs/2306.06540 |