Coordinates: | JH Michell Theatre in the Richard Berry Building |
Speaker: | Genevieve Walsh (Tufts University) |
Title: | Right-angled Coxeter groups, triangulations of spheres, and hyperbolic orbifolds |
Abstract: |
(Joint work with Sam Kim.)
Consider a right-angled Coxeter group whose defining graph is the 1-skeleton of a triangulation of S^{1} or S^{2}. Then this group is the fundamental group of a reflection orbifold which is finitely covered by a manifold. When the triangulation is an acute triangulation of S^{2}, one can form a "bouquet of hyperbolic cubes" associated to the triangulation. When the Coxeter group is a group of reflections in the faces of a right- angled hyperbolic 3-dimensional polyhedron, some bouquet of cubes is a fundamental domain for the unique hyperbolic structure. We give applications to triangulations of spheres and to the Teichmuller spaces of two-dimensional reflection orbifolds. This is joint work in progress with Sam Kim. |