|Location:||MSRI: Simons Auditorium|
A lattice is topologically locally rigid (t.l.r) if small deformations of it are isomorphic lattices. Uniform lattices in Lie groups were shown to be t.l.r by Weil [60']. We show that uniform lattices are t.l.r in any compactly generated topological group G.
A lattice is locally rigid (l.r) is small deformations arise from conjugation. It is a classical fact due to Weil [62'] that lattices in semi-simple Lie groups are l.r. Relying on our t.l.r results and on recent work by Caprace-Monod we prove l.r for uniform lattices in the isometry groups of proper geodesically complete CAT(0) spaces, with the exception of SL2(R) factors which occurs already in the classical case.
Moreover we are able to extend certain finiteness results due to Wang to this more general context of CAT(0) groups.
In the talk I will explain the above notions and results, and present some ideas from the proofs. This is a joint work with Tsachik Geladner.