Unfaithful complex hyperbolic triangle groups II: Higher order reflections

Parker, John R.; Paupert, Julien

Abstract

We consider symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2π ∕ p, with p ≥ 3. We restrict our attention to those groups where certain words are elliptic. Our goal is to find necessary conditions for such a group to be discrete. The main application we have in mind is that such groups are candidates for nonarithmetic lattices in SU(2,1).

Citation

Parker, J. R., & Paupert, J. (2009). Unfaithful complex hyperbolic triangle groups II: Higher order reflections. Pacific Journal of Mathematics, 239(2), 357-389. https://doi.org/10.2140/pjm.2009.239.357

• Journal Article Type: Article
• Publication Date: Nov 27, 2009
• Deposit Date: Oct 29, 2009
• Publicly Available Date: Dec 1, 2017
• Journal: Pacific Journal of Mathematics
• Electronic ISSN: 0030-8730
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 239
• Issue: 2
• Pages: 357-389
• DOI: https://doi.org/10.2140/pjm.2009.239.357
• Keywords: Complex reflection, Complex hyperbolic, Lattices in SU(2,1), Nonarithmetic lattice.
• Public URL: https://durham-repository.worktribe.com/output/1555503