Representation Stability for Disks in a Strip
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912926718230528 |
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| author | Wawrykow, Nicholas |
| author_facet | Wawrykow, Nicholas |
| contents | We consider the ordered configuration space of $n$ open unit-diameter disks in the infinite strip of width $w$. In the spirit of Arnol'd and Cohen, we provide a finite presentation for the rational homology groups of this ordered configuration space as a twisted algebra. We use this presentation to prove that the ordered configuration space of open unit-diameter disks in the infinite strip of width $w$ exhibits a notion of first-order representation stability similar to Church--Ellenberg--Farb and Miller--Wilson's first-order representation stability for the ordered configuration space of points in a manifold. In addition, we prove that for large $w$ this disk configuration space exhibits notions of second- (and higher) order representation stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_04678 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Representation Stability for Disks in a Strip Wawrykow, Nicholas Algebraic Topology Combinatorics Geometric Topology Representation Theory 55U15 We consider the ordered configuration space of $n$ open unit-diameter disks in the infinite strip of width $w$. In the spirit of Arnol'd and Cohen, we provide a finite presentation for the rational homology groups of this ordered configuration space as a twisted algebra. We use this presentation to prove that the ordered configuration space of open unit-diameter disks in the infinite strip of width $w$ exhibits a notion of first-order representation stability similar to Church--Ellenberg--Farb and Miller--Wilson's first-order representation stability for the ordered configuration space of points in a manifold. In addition, we prove that for large $w$ this disk configuration space exhibits notions of second- (and higher) order representation stability. |
| title | Representation Stability for Disks in a Strip |
| topic | Algebraic Topology Combinatorics Geometric Topology Representation Theory 55U15 |
| url | https://arxiv.org/abs/2301.04678 |