Deraux, Martin and Parker, John R. and Paupert, Julien (2011) 'Census of the complex hyperbolic sporadic triangle groups.', Experimental mathematics., 20 (4). pp. 467-586.
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.
|Keywords:||Complex hyperbolic geometry, Arithmeticity of lattices, Complex reflection groups.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1080/10586458.2011.565262|
|Publisher statement:||This is an Author's Accepted Manuscript of an article published in Deraux, Martin, Parker, John R. and Paupert, Julien (2011) 'Census of the complex hyperbolic sporadic triangle groups.', Experimental mathematics., 20 (4). pp. 467-586. © Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/10586458.2011.565262|
|Date accepted:||No date available|
|Date deposited:||13 February 2014|
|Date of first online publication:||2011|
|Date first made open access:||No date available|
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