Cohomology of Fuchsian groups and non-Euclidean crystallographic groups

Abstract

For each geometrically finite non-Euclidean crystallographic group (NEC group), we compute the cohomology groups. In the case where the group is a Fuchsian group, we also determine the ring structure of the cohomology. Finally, we compute the $L^2$-Betti numbers of the NEC groups.

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