A new nonarithmetic lattice in ${\rm PU}(3,1)$

Martin Deraux

doi:10.2140/agt.2020.20.925

Abstract

We study the arithmeticity of the Couwenberg–Heckman–Looijenga lattices in $PU (n, 1)$ , and show that they contain a nonarithmetic lattice in $PU (3, 1)$ which is not commensurable to the nonarithmetic Deligne–Mostow lattice in $PU (3, 1)$ .

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Martin Deraux. "A new nonarithmetic lattice in ${\rm PU}(3,1)$." Algebr. Geom. Topol. 20 (2) 925 - 963, 2020. https://doi.org/10.2140/agt.2020.20.925

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Received: 21 January 2019; Revised: 30 April 2019; Accepted: 1 July 2019; Published: 2020

First available in Project Euclid: 30 April 2020

zbMATH: 07195380

MathSciNet: MR4092315

Digital Object Identifier: 10.2140/agt.2020.20.925

Subjects:

Primary: 22E40 , 32M15

Secondary: 14N20 , 20F36 , 20F55

Keywords: Artin groups , Complex hyperbolic geometry , complex reflection groups , hyperplane arrangements , nonarithmetic lattices

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