Event

Jonah Gaster, McGill University

Wednesday, October 18, 2017 15:00to16:00
Burnside Hall Room 920, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

Sageev's cube complex dual to a collection of curves and lengths of curves on hyperbolic surfaces.

Sageev gave a very general construction of a CAT(0) cube complex dual to a `space with walls', and this construction has proved extraordinarily useful in recent celebrated work of Agol, Wise, and others. In one of the simplest nontrivial settings, this construction produces a non-positively curved cube complex dual to a finite collection of non-homotopic essential closed curves on a surface. I will show how this cube complex can be used to analyze the length function associated to a system of curves on the moduli space of hyperbolic structures on a surface of genus g, adding context to previous work of Basmajian.
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