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 H3.
Savini, A. (2023). Rigidity at infinity for the Borel function of the tetrahedral reflection lattice. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 23(4), 1583-1600 [10.2140/agt.2023.23.1583].
Rigidity at infinity for the Borel function of the tetrahedral reflection lattice
Savini A.
2023
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 H3.
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