Groups and Dynamics Seminar

Date: October 6, 2021

Time: 3:00PM - 4:00PM

Location: online

Speaker: Frank Wagner, UC Riverside

Title: Torsion Subgroups of Groups with Quadratic Dehn Function

Abstract: The Dehn function of a finitely presented group is a useful invariant closely related to the solvability of the group's word problem. It is well-known that a finitely presented group is word hyperbolic if and only if it has sub-quadratic (and thus linear) Dehn function. A result of Ghys and de la Harpe states that no hyperbolic group can contain a (finitely generated) infinite torsion subgroup. We show that this property does not carry over to classes of groups of larger Dehn function. In particular, for every m>1 and n sufficiently large (and either odd or divisible by 2^9), there exists a quasi-isometric embedding of the infinite free Burnside group B(m,n) into a finitely presented group with quadratic Dehn function.