Papers › Presentations for cusped arithmetic hyperbolic lattices
Presentations for cusped arithmetic hyperbolic lattices
Alice Mark, Julien Paupert
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We present a general method to compute a presentation for any cusped arithmetic hyperbolic lattice Γ, applying a classical result of Macbeath to a suitable Γ-invariant horoball cover of the corresponding symmetric space. As applications we compute presentations for the Picard modular groups PU(2,1,𝒪_d) for d=1,3,7 and the quaternion hyperbolic lattice PU(2,1,ℋ) with entries in the Hurwitz integer ring ℋ. The implementation of the method for these groups is computer-assisted.
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