Improving acylindrical actions on trees

Abstract: Loosely speaking, an action of a group on a tree is acylindrical if long enough paths must have small stabilisers. Groups admitting such actions form a natural subclass of acylindrically hyperbolic groups, and an interesting feature of acylindrical actions on trees is that many properties of groups are inherited from their vertex stabilisers. In order to make use of this, it is important to have some degree of control over these stabilisers. For example, can we ask for these stabilisers to be finitely generated? Even stronger, if our group is hyperbolic, can we ask for the stabilisers to be quasiconvex?

I will introduce acylindrical actions as well as some stronger and related concepts. I will also discuss a method known as the Dunwoody—Sageev resolution. We use this to move between these concepts and provide positive answers to the above questions in some cases.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.