Volume 20, issue 1 (2020)

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On the Alexander theorem for the oriented Thompson group $\vec{F}$

Valeriano Aiello

Algebraic & Geometric Topology 20 (2020) 429–438

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 (g) is L.

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Thompson group, oriented Thompson group, knots, oriented knots, oriented links, Alexander theorem, binary trees
Mathematical Subject Classification 2010
Primary: 57M25
Received: 20 November 2018
Revised: 28 March 2019
Accepted: 13 April 2019
Published: 23 February 2020
Valeriano Aiello
Section de Mathématiques
Université de Genève
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