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

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

doi:10.2140/pjm.2016.280.433

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

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

Authors

Professor John Parker j.r.parker@durham.ac.uk
Professor

Jieyan Wang

Baohua Xie

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
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.

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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.