Volume 20, issue 2 (2020)

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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 $PU\left(n,1\right)$, and show that they contain a nonarithmetic lattice in $PU\left(3,1\right)$ which is not commensurable to the nonarithmetic Deligne–Mostow lattice in $PU\left(3,1\right)$.

Keywords
complex hyperbolic geometry, nonarithmetic lattices, hyperplane arrangements, complex reflection groups, Artin groups
Mathematical Subject Classification 2010
Primary: 22E40, 32M15
Secondary: 14N20, 20F36, 20F55