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Census of the complex hyperbolic sporadic triangle groups

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

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Authors

Martin Deraux

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.

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 Mar 28, 2024
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.

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Accepted Journal Article (351 Kb)
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Copyright 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




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