On the Alexander theorem for the oriented Thompson group F

Aiello, Valeriano

doi:10.2140/agt.2020.20.429

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

Valeriano Aiello

Algebraic & Geometric Topology 20 (2020) 429–438

DOI: 10.2140/agt.2020.20.429

Abstract

Recently, Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group $\vec{F}$ . 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 $\vec{L}$ , there exists an element $g$ in $\vec{F}$ whose closure $\vec{ℒ} (g)$ is $\vec{L}$ .

Keywords

Thompson group, oriented Thompson group, knots, oriented knots, oriented links, Alexander theorem, binary trees

Mathematical Subject Classification 2010

Primary: 57M25

References

Publication

Received: 20 November 2018

Revised: 28 March 2019

Accepted: 13 April 2019

Published: 23 February 2020

Authors

Valeriano Aiello
Section de Mathématiques Université de Genève 2–4 rue du Lièvre Case Postale 64 1211 Genève 4 Switzerland

Volume 20, issue 1 (2020)