Recently, Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group . 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 , there exists an element in whose closure is .
"On the Alexander theorem for the oriented Thompson group ." Algebr. Geom. Topol. 20 (1) 429 - 438, 2020. https://doi.org/10.2140/agt.2020.20.429