Lie groups with a small space of metric structures

Date:
27.10.2022

Speaker:
Gabriel Pallier

In this talk we will consider a family of solvable, nonnilpotent Lie groups, including the threedimensional group SOL. On such a group, any pair of leftinvariant Riemannian metrics are found to be roughly similar: after multiplying one of them by a suitable multiplicative constant, they will differ by at most a bounded amount. This allows one to reformulate various earlier results about the quasi isometries of these groups in a common framework.
I will compare this result with a recent theorem of OregonReyes, giving an opposite conclusion when considering nonelementary wordhyperbolic groups: the latter are found to have large spaces of metric structures.
Joint work with Enrico Le Donne and Xiangdong Xie.