## Experimental Mathematics

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

### Census of the Complex Hyperbolic Sporadic Triangle Groups

Martin Deraux, John R. Parker, and Julien Paupert

#### 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