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Research Past Conferences and Workshops Geometry and Groups
Mini-Workshop “Geometry and Groups”
Abstract of lectures by Prof. Monod
The lectures will begin as an introduction to cat(0) spaces, also called Hadamard spaces. These spaces are defined by imposing a simple inequality on triangles in completely general metric spaces in order to imitate the notion of "non-positive sectional curvature" familiar in Riemannian geometry. That level of generality allows to produce relatively simple arguments that are interesting even for the special case of Riemannian manifolds.
We will introduce from the very beginning some of the general techniques in cat(0) geometry. Our guiding goals will be (1) to prove a splitting theorem in the spirit of Lawson-Yau and Gromoll-Wolf; (2) to prove a superrigidity theorem in the spirit of Margulis. This goals will provide motivation for the general theory.