Topology and Geometric Group Theory Seminar

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

Tuesday, March 27, 2018 - 1:30pm
Malott 203

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, Agol-Groves-Manning, etc. 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 describe 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.