The sub-linearly Morse boundary

Abstract: The Gromov boundary, of a hyperbolic metric space, plays a central role in many aspects of geometric group theory. In this talk, we introduce a generalization of the Gromov boundary that also applies to non-hyperbolic spaces. For a given proper geodesic metric space and a given sublinear function \(\kappa\), we define the \(\kappa\)-Morse boundary to be the space of all \(\kappa\)-sublinearly-Morse quasi-geodesics rays starting at a given base point.

We show that, equipped with a coarse version of the cone topology, the \(\kappa\)-boundary is metrizable and is a QI-invariant. For some groups, we show that their Poisson boundaries can be realized on the \(\kappa\)-boundary of their Cayley graphs. These groups include all \(\CAT(0)\) groups, mapping class groups, Teichmüller spaces, hierarchically hyperbolic groups, and relatively hyperbolic groups.

This talk is based on joint projects with Ilya Gekhtmann, Kasra Rafi, and Giulio Tiozzo.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( chat | slides )

---

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 five minutes after the hour. Talks are typically 55 minutes long, including time for questions.

---