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Title: Discrete complex reflection groups
in PU(2,1)
Abstract: The group PU(n,1) of holomorphic isometries of complex hyperbolic
space is one of the two occurrences (with PO(n,1)) of a simple real Lie
group of rank 1 where Margulis superrigidity does not hold. The only known
examples of nonarithmetic lattices in PU(2,1) were constructed by Mostow
in the 1980's. We will recall the construction of these lattices, which
are generated by complex reflections, and we will show how to find new
examples of the same kind in a family of configuration polygons. This is
joint work with John Parker (Durham). |