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Nonarithmetic hyperbolic manifolds and trace rings

Olivier Mila

Algebraic & Geometric Topology 18 (2018) 4359–4373

We give a sufficient condition on the hyperplanes used in the Belolipetsky–Thomson inbreeding construction to obtain nonarithmetic manifolds. We explicitly construct infinitely many examples of such manifolds that are pairwise noncommensurable and estimate their volume.

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hyperbolic manifold, nonarithmetic lattice, trace rings
Mathematical Subject Classification 2010
Primary: 53C23, 22E40
Secondary: 57M50, 51M25, 20G30
Received: 1 June 2018
Revised: 23 July 2018
Accepted: 3 August 2018
Published: 11 December 2018
Olivier Mila
Mathematisches Institut
Universität Bern