On the stabilization of the topological complexity of graph braid groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914305104936960 |
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| author | Knudsen, Ben |
| author_facet | Knudsen, Ben |
| contents | We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually stabilizes at its maximal possible value, a direct analogue of a stability phenomenon in the ordered setting first conjectured by Farber. We estimate the stable range in terms of the number of trivalent vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_04346 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the stabilization of the topological complexity of graph braid groups Knudsen, Ben Algebraic Topology Geometric Topology We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually stabilizes at its maximal possible value, a direct analogue of a stability phenomenon in the ordered setting first conjectured by Farber. We estimate the stable range in terms of the number of trivalent vertices. |
| title | On the stabilization of the topological complexity of graph braid groups |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2302.04346 |