Lecture 2: Almost filling laminations and the connectivity of ending lamination space I

Mon, 29/12/200816:00-17:30
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.