Geometry and Topology Seminar: Deligne-Mostow lattices and cone metrics on the sphere.
21 May 2015 13:00 in CM221.
Finding lattices in PU(n,1) has been one of the major challenges of the last decades. One way of constructing lattices is to give a fundamental domain for its action on the complex hyperbolic space.
One approach, successful for some lattices, consists of seeing the complex hyperbolic space as the configuration space of cone metrics on the sphere and of studying the action of some maps exchanging the cone points with same cone angle.
In this talk we will see how, in a joint work with John Parker, we extended this construction of fundamental polyhedra to all Deligne-Mostow lattices with three fold symmetry.