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Rigidity at infinity for the Borel function of the tetrahedral reflection lattice

Alessio Savini

Algebraic & Geometric Topology 23 (2023) 1583–1600
Abstract

If Γ is the fundamental group of a complete finite volume hyperbolic 3–manifold, Guilloux conjectured that the Borel function on the PSL (n, )–character variety of Γ should be rigid at infinity, that is it should stay bounded away from its maximum at ideal points.

We prove Guilloux’s conjecture in the particular case of the reflection group associated to a regular ideal tetrahedron of 3.

Keywords
tetrahedral reflection lattice, Borel function, character variety, ideal point
Mathematical Subject Classification 2010
Primary: 57T10
Secondary: 53C35, 57M27
References
Publication
Received: 11 June 2019
Revised: 29 May 2021
Accepted: 14 November 2021
Published: 14 June 2023
Authors
Alessio Savini
Section de Mathématiques
University of Geneva
Geneva
Switzerland

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