Vortrag am

Donnerstag, 4.6.2015

Martin Olbrich, Luxembourg

"Transfer operators, resonances, and group cohomology for hyperbolic manifolds of infinite volume "

"Transfer operators, resonances, and group cohomology for hyperbolic manifolds of infinite volume "

Abstract:

More than twenty years ago, Patterson gave a uniform conjectural description of the singularities of Selberg zeta functions associated to vector bundles over the sphere bundle of geometrically finite hyperbolic manifolds without cusps. 'Uniform' means in particular, that the non-canonical distinction between spectral and topological zeroes disappears. The description makes sense for all quotients of rank one symmetric spaces by discrete convex cocompact groups. It is given in terms of group cohomology with coefficients in principal series representations. Although the description is motivated by the transfer operator approach to zeta functions, in almost all cases where the conjecture has been verified so far one uses some form of a Selberg trace formula. In the talk we discuss methods how transfer operator methods might lead to a direct verification of the conjecture, at least for some cases.