Shortcut graphs and groups

Shortcut graphs are graphs in which long enough cycles cannot embed
without metric distortion. Shortcut groups are groups which act
properly and cocompactly on shortcut graphs. These notions unify a
surprisingly broad family of graphs and groups of interest in
geometric group theory and metric graph theory including: systolic and
quadric groups (in particular finitely presented C(6) and C(4)-T(4)
small cancellation groups), cocompactly cubulated groups, hyperbolic
groups, Coxeter groups and the Baumslag-Solitar group BS(1,2). Most
of these examples satisfy a strong form of the shortcut property. I
will discuss some of these examples as well as some general
constructions and properties of shortcut graphs and groups.