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Presentations for
cusped arithmetic hyperbolic lattices
Alice Mark and Julien Paupert |
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Algebraic & Geometric Topology 22 (2022) 3577–3626
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Abstract |
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We present a general method to compute a presentation for any cusped arithmetic hyperbolic lattice , applying a classical result of Macbeath to a suitable –invariant horoball cover of the corresponding symmetric space. As applications we compute presentations for the Picard modular groups for and the quaternion hyperbolic lattice with entries in the Hurwitz integer ring . The implementation of the method for these groups is computer-assisted. |
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Keywords
arithmetic lattices, group presentations, hyperbolic
geometry
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Mathematical Subject Classification 2010
Primary: 20F05, 20F65, 22E40
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References |
Publication
Received: 27 February 2018
Revised: 24 June 2021
Accepted: 20 July 2021
Published: 14 March 2023
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Authors |
| Alice Mark | |
| Department of Mathematics Vanderbilt University Nashville, TN United States |
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| Julien Paupert | |
| School of Mathematical and
Statistical Sciences Arizona State University Tempe, AZ United States |
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