Deformations of reducible representations of 3–manifold groups into $\mathrm{PSL}_2(\mathbb{C})$

Abstract

Let $M$ be a 3–manifold with torus boundary which is a rational homology circle. We study deformations of reducible representations of ${\pi }_1\left(M\right)$ into ${PSL}_2\left(ℂ\right)$ associated to a simple zero of the twisted Alexander polynomial. We also describe the local structure of the representation and character varieties.