On Jones' subgroup of R. Thompson group $F$

By Gili Golan, Mark V. Sapir. 2015

58 citations recorded by the source corpus.

Recently Vaughan Jones showed that the R. Thompson group $F$ encodes in a natural way all knots, and a certain subgroup $\vec F$ of $F$ encodes all oriented knots. We answer several questions of Jones about $\vec F$. In particular we prove that the subgroup $\vec F$ is generated by $x_0x_1, x_1x_2, x_2x_3$ (where $x_i, i=0,1,2,...$ are the standard generators of $F$) and is isomorphic to $F_3$, the analog of $F$ where all slopes are powers of $3$ and break points are $3$-adic rationals. We also show that $\vec F$ coincides with its commensurator. Hence the linearization of the permutational representation of $F$ on $F/\vec F$ is irreducible.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ae5801e3fb3fddf2a573a6168e9cc007eb36f5cd

Citations in the corpus

• On subgroups of R. Thompson's group $F$ (2015, unknown): “−→ F is isomorphic to the Thompson-Brown group F 3 [9], we have Corollary 3.16.”