Modul:   MAT075  Zurich Graduate Colloquium

What is... a convex bicombing?

Vortrag von Giuliano Basso

Datum: 20.03.18  Zeit: 17.15 - 18.30  Raum:

A bicombing on a metric space selects for every pair of points a geodesic connecting them. The existence of a bicombing satisfying a suitable convexity condition may be viewed as a weak (but non-coarse) global notion of non-positive curvature that allows for non-unique geodesics. The talk will give a survey of recent results on spaces with such a structure. For example: Every word hyperbolic group acts geometrically on a proper, finite dimensional metric space with a unique convex bicombing of the strongest type. Moreover, a metric space admits a barycenter map if and only if it admits a bicombing of the weakest convexity type.