# Bonn Topology Group - Abstracts

General Information - Members - Activities - Topology Seminar

### Talk

April 16th 2019

Giles Gardam (WWU Münster):
Boundaries of hyperbolic and CAT(0) groups and Cannon-Thurston maps.

### Abstract

A fundamental invariant in the study of hyperbolic groups is their boundaries.
The classical Cannon-Thurston map for a closed fibered hyperbolic 3-manifolds relates two such boundaries: It gives a continuous surjection from the boundary of the surface group
(a circle) to the boundary of the 3-manifold group (a 2-sphere). Mitra generalized this to all hyperbolic groups with hyperbolic normal subgroups.
I will explain why such a generalization to CAT(0) groups with the visual boundary is impossible.

Joint work with Beeker-Cordes-Gupta-Stark.

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