Work

Census of the complex hyperbolic sporadic triangle groups

Year: 2010

Type: preprint

Abstract: The goal of this paper is to give a conjectural census of complex hyperbolic sporadic 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 presentation, as well as a list of cusps and generators for their stabilisers. 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1006.3437

Authors: Deraux, Martin, Parker, John R., Paupert, Julien

Institutions: Université Joseph Fourier, Institut Fourier, Durham University, University of Utah

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Moduli Spaces, Hyperbolic Geometry, and Arithmetic Groups