Vortrag
Invariants for sublinear bilipschitz equivalence
Vortrag von Dr. Gabriel Pallier
Datum: 11.03.20 Zeit: 15.45 - 16.45 Raum: ETH HG G 43 CANCELLED
Sublinear bilipschitz equivalences between metric spaces are generalized quasiisometries. In this generalization, the large-scale Lipschitz behavior is kept, while the (uniformly) coarse behavior is not kept. These equivalences appear in the study of asymptotic cones of Lie groups by Cornulier. They occur especially between families of non-pairwise quasiisometric nilpotent or solvable connected Lie groups with close structure. In this talk, I will give an introduction to sublinear bilipschitz equivalences and report on my work on revisiting the classical quasiisometric invariants of groups to determine which of them can be turned into sublinear asymptotic invariants. This lies in continuation of Gromov's questions of classifying homogeneous spaces (e.g. Riemannian symmetric spaces and noncompact solvmanifolds) up to quasiisometry and investigate their quasiisometric rigidity. I will present a partial classification result for the Riemannian homogeneous spaces of negative curvature, and discuss the open problem of determining which groups are sublinearly bilipschitz equivalent to real hyperbolic spaces.