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2011 Census of the Complex Hyperbolic Sporadic Triangle Groups
Martin Deraux, John R. Parker, Julien Paupert
Experiment. Math. 20(4): 467-486 (2011).


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.


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Martin Deraux. John R. Parker. Julien Paupert. "Census of the Complex Hyperbolic Sporadic Triangle Groups." Experiment. Math. 20 (4) 467 - 486, 2011.


Published: 2011
First available in Project Euclid: 8 December 2011

zbMATH: 1264.22009
MathSciNet: MR2859902

Primary: 11F06 , 22E40 , 51M10

Keywords: arithmeticity of lattices , Complex hyperbolic geometry , complex reflection groups

Rights: Copyright © 2011 A K Peters, Ltd.


Vol.20 • No. 4 • 2011
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