Stefanie Zbinden

Heriot-Watt University


The contraction space and its applications


Geometry and Topology Seminar


28th January 2025, 2:00 pm – 3:00 pm
Fry Building, 2.04


In the realm of CAT(0) groups, there exists the following powerful dichotomy. Either the group has linear divergence, in which case all asymptotic cones are cut-point free, or the group has a Morse geodesic, in which case all asymptotic cones have cut-points and the group is acylindrically hyperbolic.

This talk focuses on work in progress with Cornelia Drutu and Davide Spriano, where we show that the above dichotomy holds for a larger class of groups. In particular, that it holds for groups acting coboundedly and properly on injective metric spaces and geodesic median spaces.

The main tool of the proof is the contraction space construction, a construction which assigns a hyperbolic space to any given geodesic metric space. We will introduce and motivate this construction and outline how it can be used in the proof of the dichotomy.






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