The Hilden Double Coset Problem in Braid Groups
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 particul...
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| creator | Hovland, Seth |
| description | 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 $B_n.$ |
| doi_str_mv | 10.48550/arxiv.2401.02488 |
| format | Article |
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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
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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
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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 $B_n.$</abstract><doi>10.48550/arxiv.2401.02488</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Geometric Topology Mathematics - Group Theory |
| title | The Hilden Double Coset Problem in Braid Groups |
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