Shortcut graphs and groups

We introduce shortcut graphs and groups. Shortcut are in which cycles cannot embed without metric distortion. groups act properly cocompactly on graphs. These notions unify a surprisingly broad family of interest geometric group theory graph theory, including: the 1-skeletons systolic quadric complexes (in particular finitely presented C(6) C(4)-T(4) small cancellation groups), finite dimensional CAT(0) cube complexes, hyperbolic graphs, standard Cayley generated Coxeter Baumslag-Solitar BS(1,2). Most these examples satisfy strong form property. The properties also have important theoretic consequences. show that exponential isoperimetric isodiametric functions. satisfying property polynomial