Dimension of representation and character varieties for two and three-orbifolds

Abstract

We consider varieties of representations and characters of 2 and 3-dimensional orbifolds in semisimple Lie groups, and we focus on computing their dimension. For hyperbolic 3-orbifolds, we consider the component of the variety of characters that contains the holonomy composed with the principal representation, we show that its dimension equals half the dimension of the variety of characters of the boundary. We also show that this is a lower bound for the dimension of generic components. We furthermore provide tools for computing dimensions of varieties of characters of 2-orbifolds, including the Hitchin component. We apply this computation to the dimension growth of varieties of characters of some 3-dimensional manifolds in SL(n,C).

arXiv comment47 pages, 9 Figures

References in corpus (6)

• Generators, Relations and Symmetries in Pairs of 3x3 Unimodular Matrices
• Poisson Geometry of SL(3,C)-Character Varieties Relative to a Surface with Boundary
• Topology of Moduli Spaces of Free Group Representations in Real Reductive Groups
• Local coordinates for SL(n,C) character varieties of finite volume hyperbolic 3-manifolds
• Representations of knot groups into ${\mathrm{SL}}_n(\mathbf{C})$ and twisted Alexander polynomials
• Holomorphic volume forms on representation varieties of surfaces with boundary

Cited by in corpus (1)

• On the topology of character varieties of once-punctured torus bundles