Presentations for cusped arithmetic hyperbolic lattices

Alice Mark, Julien Paupert

Research output: Contribution to journalArticlepeer-review


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; Od) 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.

Original languageEnglish (US)
Pages (from-to)3577-3626
Number of pages50
JournalAlgebraic and Geometric Topology
Issue number8
StatePublished - 2022
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology


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