Geometry and Topology Seminar: Complex hyperbolic triangle groups
8 October 2015 13:00 in CM221.
It is well known that the group generated by reflections in the sides
of a hyperbolic triangle is rigid, even when embedded in the isometry
group of higher dimensional hyperbolic space. However it is possible
to deform such a group when it is embedded in the isometry group of
complex hyperbolic space. In his ICM talk, Rich Schwartz gave a series
of conjectures about such groups. In particular, he conjectured that
discreteness of these representations is controlled by a particular
element. In this talk I will give a survey of the topic and then
discuss certain cases where Schwartz's conjecture is true. This is
joint work with Jieyan Wang and Baohua Xie and with Pierre Will.