Geodesic
On the Alexander theorem for the oriented Thompson group F
Aiello, Valeriano1
1Section de Mathématiques, Université de Genève, 2–4 rue du Lièvre, Case Postale 64, 1211 Genève 4, Switzerland
Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 429-438
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Recently, Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group F→. Here we prove, by analogy with Alexander’s classical theorem establishing that every knot or link can be represented as a closed braid, that, given an oriented knot/link L→, there exists an element g in F→ whose closure ℒ→(g) is L→.

DOI : 10.2140/agt.2020.20.429
Classification : 57M25
Keywords: Thompson group, oriented Thompson group, knots, oriented knots, oriented links, Alexander theorem, binary trees

Aiello, Valeriano  1

1 Section de Mathématiques, Université de Genève, 2–4 rue du Lièvre, Case Postale 64, 1211 Genève 4, Switzerland 
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Aiello, Valeriano. On the Alexander theorem for the oriented Thompson group F. Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 429-438. doi: 10.2140/agt.2020.20.429

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