A new nonarithmetic lattice in PU(3,1)

Deraux, Martin

doi:10.2140/agt.2020.20.925

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

Martin Deraux

Algebraic & Geometric Topology 20 (2020) 925–963

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 $PU (3, 1)$ .

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

Volume 20, issue 2 (2020)