Rigidity of representations in SO(4,1) for Dehn fillings on 2-bridge knots

TL;DR

The paper proves that many Dehn fillings on hyperbolic 2-bridge knots are rigid in SO(4,1), meaning their representations are conjugate to the hyperbolic structure, with local rigidity for most fillings.

Contribution

It establishes infinite rigidity results for Dehn fillings on 2-bridge knots in the context of SO(4,1), extending understanding of geometric structures and representations.

Findings

Infinitely many Dehn fillings are rigid in SO(4,1)

Any discrete faithful representation is conjugate to the hyperbolic holonomy

Most Dehn fillings exhibit local rigidity

Abstract

We prove that, for a hyperbolic two bridge knot, infinitely many Dehn fillings are rigid in $SO_0(4,1)$. Here rigidity means that any discrete and faithful representation in $SO_0(4,1)$ is conjugate to the holonomy representation in $SO_0(3,1)$. We also show local rigidity for almost all Dehn fillings.