The Ending Lamination Conjecture was one of the central problems in the theory of 3-manifolds and its resolution in the 2000s by Brock–Canary–Minsky stands as a milestone in the classification of hyperbolic 3-manifolds. The proof required a deep understanding of the space of ending laminations and combined a wide range of ideas and techniques, many of which continue to play a crucial role across current research areas.

In this reading seminar, we will study the topological properties of the space of ending laminations, following Gabai’s 2008 paper [1]. Our second meeting will continue our discussion on the hyperbolicity of curve graph, and we will revisit the notion of measured lamination and foliation.