Algebraic & Geometric Topology

Nonarithmetic hyperbolic manifolds and trace rings

Olivier Mila

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Abstract

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.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 4359-4373.

Dates
Received: 1 June 2018
Revised: 23 July 2018
Accepted: 3 August 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.agt/1545102074

Digital Object Identifier
doi:10.2140/agt.2018.18.4359

Mathematical Reviews number (MathSciNet)
MR3892248

Zentralblatt MATH identifier
07006394

Subjects
Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds 51M25: Length, area and volume [See also 26B15] 20G30: Linear algebraic groups over global fields and their integers

Keywords
hyperbolic manifold nonarithmetic lattice trace rings

Citation

Mila, Olivier. Nonarithmetic hyperbolic manifolds and trace rings. Algebr. Geom. Topol. 18 (2018), no. 7, 4359--4373. doi:10.2140/agt.2018.18.4359. https://projecteuclid.org/euclid.agt/1545102074


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