Remarks on some maximal subgroups of the Thompson group $F$ and the $\vec{F}$-index of knots
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 at most by $3$ after changing the orientation of a knot.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Operator Algebra Research
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Revista de la Unión Matemática Argentina
- Pages
- 443–458
- Publication date
- 14 April 2026
- Language
- EN