Representation asymptotics in the homology of pure graph braid groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866916981781823488 |
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| author | Hainaut, Louis Knudsen, Ben Wawrykow, Nicholas |
| author_facet | Hainaut, Louis Knudsen, Ben Wawrykow, Nicholas |
| contents | We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explicit formulas for the asymptotic multiplicities in homology of many irreducible representations of the symmetric group, in the spirit of representation stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation asymptotics in the homology of pure graph braid groups Hainaut, Louis Knudsen, Ben Wawrykow, Nicholas Algebraic Topology Geometric Topology We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explicit formulas for the asymptotic multiplicities in homology of many irreducible representations of the symmetric group, in the spirit of representation stability. |
| title | Representation asymptotics in the homology of pure graph braid groups |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2510.00201 |