Cross ratios on Furstenberg boundaries

Vortrag von Dr. Jonas Beyrer

Datum: 08.11.17  Zeit: 15.45 - 16.45  Raum: ETH HG G 43

A rank one symmetric space of non-compact type carries naturally a cross ratio on its visual boundary, which has many interesting applications. In particular the cross ratio characterizes the isometry group by its boundary action. We will use a similar geometric construction as for a rank one space to define cross ratios on Furstenberg boundaries of higher rank symmetric spaces of non-compact type. By showing several properties of those cross ratios, in particular that they characterize the isometry group of the symmetric space, we motivate that we get a reasonable generalization of the rank one case.