Census of the complex hyperbolic sporadic triangle groups

Deraux, Martin; Parker, John R; Paupert, Julien

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.

Citation

Deraux, M., Parker, J. R., & Paupert, J. (2011). Census of the complex hyperbolic sporadic triangle groups. Experimental Mathematics, 20(4), 467-586. https://doi.org/10.1080/10586458.2011.565262

• Journal Article Type: Article
• Publication Date: Nov 28, 2011
• Deposit Date: Mar 16, 2012
• Publicly Available Date: Feb 13, 2014
• Journal: Experimental Mathematics
• Print ISSN: 1058-6458
• Electronic ISSN: 1944-950X
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Issue: 4
• Pages: 467-586
• DOI: https://doi.org/10.1080/10586458.2011.565262
• Keywords: Complex hyperbolic geometry, Arithmeticity of lattices, Complex reflection groups.
• Public URL: https://durham-repository.worktribe.com/output/1478945