This is joint work with Marc Burger and Alessandra Iozzi
Abstract: Let G be a lattice in SO(n,1) and let h:G --> SO(n,1) be any representation. For cocompact lattices, the volume of a representation is an invariant whose maximal and rigidity properties have been studied extensively. We will show how to define the volume of a representation in the non cocompact case (a different definition by Francaviglia and Klaff also exists). In particular, we establish a rigidity result for maximal representations, recovering Mostow rigidity for hyperbolic manifolds. In the cocompact case, the set of values for the volume of a representation is discrete. In even dimension, this follows from the fact that the volume form is an Euler class. In odd dimension, this was proven by Besson, Courtois and Gallot. The situation changes in the noncocompact case and for example the discreteness of the set of value is not valid anymore in dimension 2 and 3. We prove that in even dimension greater or equal to 4, the set of value of the volume of a representation is, up to a universal constant, an integer.
Dienstag, den 26. November 2013 um 13:30 Uhr, in INF 288, HS 5 Dienstag, den 26. November 2013 at 13:30, in INF 288, HS 5
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Professor Dr. Anna Wienhard