#### Volume 20, issue 1 (2020)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
On the Alexander theorem for the oriented Thompson group $\vec{F}$

### Valeriano Aiello

Algebraic & Geometric Topology 20 (2020) 429–438
##### Abstract

Recently, Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group $\stackrel{\to }{F}\phantom{\rule{-0.17em}{0ex}}$. 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 $\stackrel{\to }{L}$, there exists an element $g$ in $\stackrel{\to }{F}$ whose closure $\stackrel{\to }{\mathsc{ℒ}}\left(g\right)$ is $\stackrel{\to }{L}$.

##### Keywords
Thompson group, oriented Thompson group, knots, oriented knots, oriented links, Alexander theorem, binary trees
Primary: 57M25