Deforming reducible representations of surface and 2-orbifold groups

Abstract

For a compact 2-orbifold with negative Euler characteristic ${\mathcal{O}}^2$, the variety of characters of $\ddot{I}{€}_1({\mathcal{O}}^2)$ in ${\mathrm{SL}}_n(\mathbb{R})$ is a non-singular manifold at $\mathbb{C}$-irreducible representations. In this paper we prove that when a $\mathbb{C}$-irreducible representation of $\ddot{I}{€}_1({\mathcal{O}}^2)$ in ${\mathrm{SL}}_n(\mathbb{R})$ is viewed in ${\mathrm{SL}}_{n+1}(\mathbb{R})$, then the variety of characters is singular, and we describe the singularity.

Version 2: Minor corrections and more details in Section 5