Experimental Mathematics

Census of the Complex Hyperbolic Sporadic Triangle Groups

Martin Deraux, John R. Parker, and Julien Paupert

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Abstract

The goal of this paper is to give a conjectural census of complex hyperbolic sporadic triangle groups. We prove that only finitely many of these sporadic groups are lattices.

We also give a conjectural list of all lattices among sporadic groups, and for each group in the list we give a conjectural group presentation, as well as a list of cusps and generators for their stabilizers. We describe strong evidence for these conjectural statements, showing that their validity depends on the solution of reasonably small systems of quadratic inequalities in four variables.

Article information

Source
Experiment. Math., Volume 20, Issue 4 (2011), 467-486.

Dates
First available in Project Euclid: 8 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.em/1323367158

Mathematical Reviews number (MathSciNet)
MR2859902

Zentralblatt MATH identifier
1264.22009

Subjects
Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 11F06: Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] 51M10: Hyperbolic and elliptic geometries (general) and generalizations

Keywords
Complex hyperbolic geometry arithmeticity of lattices complex reflection groups

Citation

Deraux, Martin; Parker, John R.; Paupert, Julien. Census of the Complex Hyperbolic Sporadic Triangle Groups. Experiment. Math. 20 (2011), no. 4, 467--486. https://projecteuclid.org/euclid.em/1323367158


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