|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|
(Joint work with Sam Kim.)
Consider a right-angled Coxeter group whose defining graph is the 1-skeleton of a triangulation of S1 or S2. 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 S2, 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.