Local-to-global rigidity
It is well-known that a simply connected homogeneous Riemannian manifold satisfies the following « local-to-global rigidity » property: any simply connected Riemannian manifold N whose balls of radius 1 are isometric to the ball of radius 1 of M must be isometric to M. In this talk we shall study this property in the setting of vertex-transitive graphs. In particular, we characterize local-to-global rigid building among those of SL(n,K) where K is a local field (not necessarily commutative).
This is a joint work with Mikael de la Salle.