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

Savini, Alessio

doi:10.2140/agt.2023.23.1583

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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

DOI: 10.2140/agt.2023.23.1583

Abstract

If $Γ$ is the fundamental group of a complete finite volume hyperbolic $3$ –manifold, Guilloux conjectured that the Borel function on the $PSL (n, ℂ)$ –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 $ℍ^{3}$ .

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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Volume 23, issue 4 (2023)