New non-arithmetic complex hyperbolic lattices

Deraux, Martin; Parker, John R.; Paupert, Julien

Abstract

We produce a family of new, non-arithmetic lattices in TeX. All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne–Mostow, and fell into nine commensurability classes. Our groups produce five new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for constructing fundamental domains for discrete groups acting on the complex hyperbolic plane.

Citation

Deraux, M., Parker, J. R., & Paupert, J. (2016). New non-arithmetic complex hyperbolic lattices. Inventiones Mathematicae, 203(3), 681-771. https://doi.org/10.1007/s00222-015-0600-1

• Journal Article Type: Article
• Acceptance Date: Apr 17, 2015
• Online Publication Date: May 8, 2015
• Publication Date: Mar 1, 2016
• Deposit Date: Apr 21, 2015
• Publicly Available Date: May 8, 2016
• Journal: Inventiones Mathematicae
• Print ISSN: 0020-9910
• Electronic ISSN: 1432-1297
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 203
• Issue: 3
• Pages: 681-771
• DOI: https://doi.org/10.1007/s00222-015-0600-1
• Related Public URLs: http://arxiv.org/abs/1401.0308