The boundary of the arc complex

Dr S. Schleimer (University of Warwick)

Monday 3rd December, 2012 16:00-17:00 417


Klarreich proved that the boundary of the curve complex is (equivarently) homeomorphic to the space of ending laminations. We have found (partly following Hamenstadt) a new proof of this using the language of train tracks. Our techniques also allow us to compute the boundary of the arc complex. This time it is the union of spaces of ending laminations in so-called "holes": subsurfaces that see all arcs. This is partly joint work with Alex Wickens. I'll start the talk by reviewing the definitions of the curve complex, the arc complex, and the space of ending laminations. Then I'll define train-tracks and their vertex sets and define the map from ending laminations to the boundary of the curve complex. If time permits I'll also sketch why the map is open. Well-definedness, injectivity, surjectivity, and continuity will be left for the question period.

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