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    Bielliptic ball quotient compactifications and lattices in PU(2, 1) with finitely generated commutator subgroup

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    Genre
    Pre-print
    Date
    2017-01-01
    Author
    Di Cerbo, LF
    Stover, M
    Subject
    Ball quotients and their compactifications
    volumes of complex hyperbolic manifolds
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/4983
    
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    DOI
    10.5802/aif.3083
    Abstract
    © Association des Annales de l'institut Fourier, 2017. We construct two infinite families of ball quotient compactifications birational to bielliptic surfaces. For each family, the volume spectrum of the associated noncompact finite volume ball quotient surfaces is the set of all positive integral multiples of 8/3 π2, i.e., they attain all possible volumes of complex hyperbolic 2-manifolds. The surfaces in one of the two families all have 2-cusps, so that we can saturate the entire volume spectrum with 2-cusped manifolds. Finally, we 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.
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    Annales de l'Institut Fourier
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/4965
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