Abstract:
A property of geodesic metric spaces, called the road trip property, that generalizes hyperbolic and convex metric spaces is introduced. This property is shown to be invariant under quasi-isometry. Thus, it leads to a geometric property of finitely generated groups, also called the road trip property. The main result is that groups with the road trip property are finitely presented and satisfy a quadratic isoperimetric inequality. Examples of groups with the road trip property include hyperbolic, semihyperbolic, automatic, and CAT(0) groups.
