Complex hyperbolic (3,3,n)-triangle groups

Parker, John R.; Wang, Jieyan; Xie, Baohua

Abstract

Let p,q,rp,q,r be positive integers. Complex hyperbolic (p,q,r)(p,q,r) triangle groups are representations of the hyperbolic (p,q,r)(p,q,r) reflection triangle group to the holomorphic isometry group of complex hyperbolic space H2CHℂ2, where the generators fix complex lines. In this paper, we obtain all the discrete and faithful complex hyperbolic (3,3,n)(3,3,n) triangle groups for n≥4n≥4. Our result solves a conjecture of Schwartz in the case when p=q=3p=q=3.

Citation

Parker, J. R., Wang, J., & Xie, B. (2016). Complex hyperbolic (3,3,n)-triangle groups. Pacific Journal of Mathematics, 280(2), 433-453. https://doi.org/10.2140/pjm.2016.280.433

• Journal Article Type: Article
• Acceptance Date: Jul 2, 2015
• Online Publication Date: Jan 28, 2016
• Publication Date: Jan 28, 2016
• Deposit Date: Jan 27, 2016
• Publicly Available Date: Jan 27, 2016
• Journal: Pacific Journal of Mathematics
• Electronic ISSN: 0030-8730
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 280
• Issue: 2
• Pages: 433-453
• DOI: https://doi.org/10.2140/pjm.2016.280.433
• Keywords: Complex hyperbolic geometry, Complex hyperbolic triangle groups.
• Public URL: https://durham-repository.worktribe.com/output/1421795