### Strongly shortcut spaces

Geometry and Topology Seminar

15th December 2020, 2:00 pm – 3:00 pm

Zoom seminar, if interested, please email one of the organisers to gain access to the Zoom link

The strong shortcut property was introduced in my PhD thesis as

a very general nonpositive curvature condition for graphs.

Despite unifying many important classes of graphs in geometric

group theory and metric graph theory, strongly shortcut graphs

have strong algebraic consequences for groups that act on them

properly and cocompactly, including finite presentedness and

polynomial isoperimetric (Dehn) function.

In recent work I have generalized the strong shortcut condition

to rough geodesic metric spaces. In this talk I will define

strongly shortcut metric spaces, describe various

characterizations and properties of them and relate them to

strongly shortcut groups. Using these results, I will show that

new families of groups act properly and cocompactly on strongly

shortcut graphs.

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