CASE WESTERN RESERVE UNIVERSITY

STATISTICS COLLOQUIUM

Recent cosmological observations suggest that the energy density in the universe is such that geometry of the universe is one of constant negative cur- vat ure, with an intrinsic curvature scale, ~ that is within the observable horizon. Three-dimensional manifolds of constant negative curvature come in an infinite number of possible topologies. Most interesting are the count able infinity of such manifolds with finite volume, in particular the large (but finite) number with volume less than or equal to a few times Rc3urv Previous searches for topology have focussed on properties which are specific to one particular topology with flat geometry. I will describe a strategy for looking for topology generically, and the statistic we have devised to implement this strategy.