arXiv subjects
Publications and source records attributed to Ryan Seelig.
A simple Ore forest-skein category produces three infinite groups analogous to Richard Thompson's groups F,T,V. We prove that reconstruction theorems of McCleary and Rubin apply to them: each of these groups encodes a canonical action by homeomorphisms. This provides powerful invariants that we use to distinguish infinitely many explicit simple groups that are finitely presented (of type $F_\infty$).
We construct an explicit infinite family of pairwise non-isomorphic infinite simple groups of type $\mathrm{F}_\infty$ (in particular, they are finitely presented) that act faithfully on the circle by orientation-preserving homeomorphisms, but that admit no non-trivial piecewise affine nor piecewise projective actions on the projective line. Our examples are certain forest-skein groups which, informally, are a mixture of Richard Thompson's groups with Vaughan Jones' planar algebras.
An Ore forest-skein category provides three forest-skein groups equipped with a powerful diagrammatic calculus analogous to Richard Thompson's groups F,T,V. We investigate when forest-skein groups have simple derived subgroups and establish two characterisations: a dynamical one and a categorical one. We then construct two classes of examples. The first associates two finitely presented simple groups to every finite binary tree and the second associates two simple groups to every n-ary Higman-Thompson group.