Group Theory Seminar
The Dehn functions of subgroups in a direct product of free groups
Speaker: Dario Ascari (UPV)Date: Thursday, 20 February 2025 - 11:00Place: Aula Naranja, ICMAT
Abstract:
Subgroups in a direct product of free groups form a widely-studied family of groups, whose algebraic structure is strongly related to the finiteness properties that they satisfy. We investigate the Dehn function of such groups; this is an algebraic invariant which represents the complexity of solving the word problem. We show that, for subgroups of type \(F_{n-1}\) inside a product of \(n\) free groups, the Dehn functions have a uniform upper bound of \(N^9\). We also prove that the Bridson-Dison group has Dehn function exactly \(N^4\); the lower bound is proved through a new homotopical invariant encoded in braid groups.
