Geometry and rigidity of quasiisometries of horospherical products

Venue:
Building 20.30, Room 2.058

Date:
27.04.2023
 Speaker:

Time:
15:45

Abstract: Horospherical products of two Gromov hyperbolic spaces where introduced to unify the construction of metric spaces such as DiestelLeader graphs, the Sol geometry or treebolic spaces. In this talk we will first recall all the bases required to construct these horospherical products, then we will study their large scale geometry through a description of their geodesics and visual boundary.
Afterwards we will get interested in a geometric rigidity property of their quasiisometries. This result will lead us to a description of the quasiisometry group of solvable Lie groups constructed as horospherical products and to a new quasiisometry classification for some solvable Lie groups.