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

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

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


Jieyan Wang

Baohua Xie


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.


Parker, J. R., Wang, J., & Xie, B. (2016). Complex hyperbolic (3,3,n)-triangle groups. Pacific Journal of Mathematics, 280(2), 433-453.

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
Publisher Mathematical Sciences Publishers (MSP)
Peer Reviewed Peer Reviewed
Volume 280
Issue 2
Pages 433-453
Keywords Complex hyperbolic geometry, Complex hyperbolic triangle groups.


Accepted Journal Article (374 Kb)

Copyright Statement
First published in Pacific journal of mathematics in Vol. 280 (2016), No. 2, 433-453, published by Mathematical Sciences Publishers. © 2016 Mathematical Sciences Publishers. All rights reserved.

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