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

Parker, John R. and Wang, Jieyan and Xie, Baohua (2016) 'Complex hyperbolic (3,3,n)-triangle groups.', Pacific journal of mathematics., 280 (2). pp. 433-453.

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.

Item Type:Article
Keywords:Complex hyperbolic geometry, Complex hyperbolic triangle groups.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.2140/pjm.2016.280.433
Publisher 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.
Date accepted:02 July 2015
Date deposited:27 January 2016
Date of first online publication:28 January 2016
Date first made open access:No date available

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