Census of the complex hyperbolic sporadic triangle groups

Martin Deraux, John R. Parker, Julien Paupert

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)467-486
Number of pages20
JournalExperimental Mathematics
Issue number4
StatePublished - Nov 28 2011
Externally publishedYes


  • arithmeticity of lattices
  • complex hyperbolic geometry
  • complex reflection groups

ASJC Scopus subject areas

  • General Mathematics


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