New non-arithmetic complex hyperbolic lattices

Martin Deraux; John R. Parker; Julien Paupert

doi:10.1007/s00222-015-0600-1

New non-arithmetic complex hyperbolic lattices

Martin Deraux, John R. Parker, Julien Paupert

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

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14 Scopus citations

Abstract

We produce a family of new, non-arithmetic lattices in (Formula presented.). 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.

Original language	English (US)
Pages (from-to)	681-771
Number of pages	91
Journal	Inventiones Mathematicae
Volume	203
Issue number	3
DOIs	https://doi.org/10.1007/s00222-015-0600-1
State	Published - Mar 1 2016

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ASJC Scopus subject areas

Mathematics(all)

Cite this

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

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10.1007/s00222-015-0600-1