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On the volume spectrum of ball quotient surfaces

Posted in
Speaker: 
Luca Di Cerbo
Affiliation: 
MPIM
Date: 
Tue, 12/01/2016 - 12:15 - 12:45
Location: 
MPIM Lecture Hall

I will construct two infinite families of noncompact complex hyperbolic 2-manifolds
whose volume spectrum is the set of all integral multiples of 8/3\pi^{2}, i.e., they
both saturate the volume spectrum of ball quotient surfaces. The surfaces in one of
the two families have all 2-cusps, so that one can saturate the entire volume spectrum
with 2-cusped manifolds.  Finally, I show that the associated neat lattices
have infinite abelianization and finitely generated commutator subgroup.
These appear to be the first known nonuniform lattices in PU(2, 1), and
the first infinite tower, with this property. Joint work with M. Stover.

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