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

Martin Deraux

Algebraic & Geometric Topology 20 (2020) 925–963

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