Revista de la
Unión Matemática Argentina
Remarks on some maximal subgroups of the Thompson group $F$ and the $\vec{F}$-index of knots
Valeriano Aiello

Volume 69, no. 2 (2026), pp. 443–458    

Published online (final version): July 9, 2026

https://doi.org/10.33044/revuma.5585

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Abstract

We demonstrate that three maximal subgroups of infinite index in the rectangular subgroup $K_{(2,2)}$ of the Thompson group $F$, each containing Jones's 3-colorable subgroup $\mathcal{F}$, can be characterized as stabilizer subgroups. Additionally, we show that the $\vec{F}$-index, an elementary knot invariant introduced thanks to Jones's construction of knots from Thompson groups, may increase by at most 3 after changing the orientation of a knot.

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