`The cohomology groups of certain quotients of products of upper half planes and upper half spaces'

Abstract:
A theorem of Matsushima-Shimura shows that the the space of
harmonic differential forms on the quotient of products of upper half
planes under the action of certain groups, when the quotient is compact,
is the direct sum of two subspaces called the universal and cuspidal
subspaces. We generalize this result to compact quotients of products of
upper half planes and upper half spaces (hyperbolic three spaces) under
the action of certain groups to obtain a similar decomposition. Using
Hodge theory, one gets information about the cohomology groups of such
quotients. This is joint work with Lydia Eldredge.