Seminario Teoría de Grupos
Reducing rooted graphs while preserving their Higman-Thompson groups
Ponente: Roman Gorazd (University of Newcastle, Australia)Fecha: jueves 13 de febrero de 2025 - 11:00Lugar: Aula Naranja, ICMAT
Resumen:
The Higman-Thompson groups are dense subgroups of the almost automorphism groups of quasi-regular trees that are finitely presented and (virtually) simple. Their isomorphism problem was solved by Pardo using the Leavitt algebra. In this talk, I will focus on a generalization of Higman-Thompson groups onto unfolding trees of rooted directed graphs. I will showcase certain reductions of graphs that preserve the Higman-Thompson group of its unfolding tree. The proofs that these reductions preserve the Higman-Thompson groups use the graph monoid and the Leavitt path algebra of a graph. I will also demonstrate when such unfolding trees have finite automorphism orbits(i.e. are cocompact).
