Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Dynamics, Geometry, & Groups Seminar


Thursday, January 21st, 2021

Time: 1:30 p.m Place:

Speaker: Macarena Arenas (University of Cambridge)

Title: Linear isoperimetric functions for surfaces in hyperbolic groups.

Abstract: One of the main characterisations of word-hyperbolic groups is that they are the groups with a linear isoperimetric function. That is, for a compact 2-complex X, the hyperbolicity of its fundamental group is equivalent to the existence of a linear isoperimetric function for disc diagrams D -->X.
It is likewise known that hyperbolic groups have a linear annular isoperimetric function and a linear homological isoperimetric function. I will talk about these isoperimetric functions, and about a (previously unexplored) generalisation to all homotopy types of surface diagrams. This is joint work with Dani Wise.