Configuration spaces of disks in a strip, twisted algebras, persistence, and other stories
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866914719090081792 |
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| author | Alpert, Hannah Manin, Fedor |
| author_facet | Alpert, Hannah Manin, Fedor |
| contents | We give $\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\operatorname{config}(n,w)$ of $n$ unit disks in an infinite strip of width $w$, first studied by Alpert, Kahle and MacPherson. We also study the way these spaces evolve both as $n$ increases (using the framework of representation stability) and as $w$ increases (using the framework of persistent homology). Finally, we include some results about the cup product in the cohomology and about the configuration space of unordered disks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_04574 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Configuration spaces of disks in a strip, twisted algebras, persistence, and other stories Alpert, Hannah Manin, Fedor Algebraic Topology Combinatorics Representation Theory 55R80 (18A25) We give $\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\operatorname{config}(n,w)$ of $n$ unit disks in an infinite strip of width $w$, first studied by Alpert, Kahle and MacPherson. We also study the way these spaces evolve both as $n$ increases (using the framework of representation stability) and as $w$ increases (using the framework of persistent homology). Finally, we include some results about the cup product in the cohomology and about the configuration space of unordered disks. |
| title | Configuration spaces of disks in a strip, twisted algebras, persistence, and other stories |
| topic | Algebraic Topology Combinatorics Representation Theory 55R80 (18A25) |
| url | https://arxiv.org/abs/2107.04574 |