Geometry and Topology Seminar: Non-arithmetic lattices in SU(2,1)
30 January 2014 13:00 in CM221
A lattice in a Lie group is a discrete group with finite volume quotient.
An arithmetic group is a group that is discrete essentially because the
integers are discrete in the real numbers. Arithmetic groups are lattices,
but not all lattices are arithmetic. The only Lie groups possibly containing
non-arithmetic lattices are SO(n,1) and SU(n,1) and in the latter case it
is an open question for n at least 4. From work of Deligne and Mostow in 1986 there are nine examples in SU(2,1) and one in SU(3,1). This talk is
the first of two where I will describe joint work with Deraux and Paupert
where we construct ten new examples in SU(2,1). These are the first new
examples to be found since the work of Deligne and Mostow. In the first
talk I will give the background and outline the results. In the second I
will describe the construction of five of the examples.