The current post is based on a talk I gave at the university of Leiden which unfortunately I completely butchered due, in part, to the sudden realization that I had not chance to get through this material in the given time. Nothing here is new or proved, though some sketches are added when I find it relevant.
The (unattained) goal of the presentation was to show how much of the geometry of a symmetric space of noncompact type can be determined from it boundary sphere alone (in rank 1 cases) and a simplicial complex called the boundary at infinity (in higher rank cases) by following the evolution of the Mostow rigidity theorem from its origins (closed quotients of real hyperbolic spaces) to higher ranks.
Continue reading “The rigid world of symmetric spaces of noncompact type”
-space of various types.