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 first meeting will be devoted to some of the preliminary notions used in the paper, including laminations and foliations, the weak Hausdorff topology, and the curve complex.

Reference:
1. David Gabai. On the topology of ending lamination space. Geometry & Topology, 2008, Vol. 12, pp. 1387–1424.
DOI: 10.2140/gt.2008.12.1387