Prof. David Gabai (Princeton)
Laminations (i.e. foliations of closed subspaces) of surfaces play a central role in Thurston's theory of surfaces as well as in the theory of hyperbolic 3-manifolds. For example, the closure of the space of simple closed curves on a surface is the space of projective measured laminations. We show that if the hyperbolic surface S is not the 3 or 4 holed sphere or one holed torus, then the space of ending laminations (i.e. those with each leaf dense and "fill up" S) is connected, locally path connected and cyclic.