The Hilden Double Coset Problem in Braid Groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910534546227200 |
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| author | Hovland, Seth |
| author_facet | Hovland, Seth |
| contents | In this paper we provide a solution to the double coset problem for the braid group $B_n$ modulo the Hilden subgroup $H_n.$ This result demonstrates that, as in the case of braid closures, the Link Problem for plat closures is "stably equivalent" to a solvable algebraic problem. A particularly interesting feature of the proof is that, like Garside's solutions to the Word and Conjugacy Problems, it too relies on Garside's decomposition of braids in $B_n.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02488 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hilden Double Coset Problem in Braid Groups Hovland, Seth Geometric Topology Group Theory In this paper we provide a solution to the double coset problem for the braid group $B_n$ modulo the Hilden subgroup $H_n.$ This result demonstrates that, as in the case of braid closures, the Link Problem for plat closures is "stably equivalent" to a solvable algebraic problem. A particularly interesting feature of the proof is that, like Garside's solutions to the Word and Conjugacy Problems, it too relies on Garside's decomposition of braids in $B_n.$ |
| title | The Hilden Double Coset Problem in Braid Groups |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2401.02488 |