Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 167

Fuchsian groups of the second kind and representations carried by the limit set

U. Bunke, M. Olbrich

We compute the cohomology of a Fuchsian group of the second kind with coefficients in the hyperfunction vectors of a principal series representation of SL(2,R) in terms of the scattering matrix, L2-eigenfunctions, and topological data of the corresponding hyperbolic surface. In particular, we show that these cohomology groups are finite-dimensional and have vanishing Euler characteristic.

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