Almost minimal laminations and the connectivity of ending lamination space

Almost minimal laminations and the connectivity of ending lamination space

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David Gabai, Princeton University
Fine Hall 314

We show that if S is a finite type hyperbolic surface which is not the 3 or 4-holed sphere or 1-holed torus, then the Ending lamination space of S is connected, locally path connected and cyclic. Using Klarrich's theorem this implies that the boundary of a curve complex associated to any such space is connected, locally path connected and cyclic.