The Dehn function of subgroups of direct products of free groups (Dario Ascari, University of the Basque Country)

13.05.2025 10:30

Subgroups of direct products of free groups can be very wild in general; however, they become much more controlled once they are required to satisfy some finiteness condition. We investigate the Dehn function of such groups, an isoperimetric inequality which describes the complexity of solving the word problem. We show that, for subgroups of type F_{n-1} in a product of n factors, there is a uniform polynomial bound of N^9 on all the Dehn functions. We also show an example of a subgroup whose Dehn function is exactly N^4; the computation is based on an invariant built using braid groups.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 13.05.2025, Séminaire "Groupes et géométrie"

entrée libre