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

Valeriano Aiello

doi:10.2140/agt.2020.20.429

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arXiv · 1811.08323

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

Valeriano Aiello

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Abstract

In [Jo14] and [Jo18] Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group $\vec{F}$. In this paper 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 $\vec{\mathcal{L}}(g)$ is $\vec L$.

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BibTeX RIS

Valeriano Aiello. 2018-11-20. On the Alexander Theorem for the oriented Thompson group $\vec{F}$. https://doi.org/10.2140/agt.2020.20.429

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