Title: Cohomology of Fuchsian groups and non-Euclidean 
crystallographic groups

Author: Sam Hughes

Affiliation: University of Southampton

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.