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

Martin Deraux

Algebraic & Geometric Topology 20 (2020) 925–963
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).

Keywords
complex hyperbolic geometry, nonarithmetic lattices, hyperplane arrangements, complex reflection groups, Artin groups
Mathematical Subject Classification 2010
Primary: 22E40, 32M15
Secondary: 14N20, 20F36, 20F55
References
Publication
Received: 21 January 2019
Revised: 30 April 2019
Accepted: 1 July 2019
Published: 23 April 2020
Authors
Martin Deraux
Institut Fourier
Université Grenoble Alpes
Gières
France