Dimension of representation and character varieties for two- and three-orbifolds (Q2092751)

The author studies varieties of representations and characters of 2 and 3-dimensional orbifolds in semisimple Lie groups and focuses on computing their dimension. For hyperbolic 3-orbifolds, he considers the component of the variety of characters that contains the holonomy composed with the principal representation. The author shows that its dimension equals half the dimension of the variety of characters of the boundary, and that this is a lower bound for the dimension of generic components. He also provides tools for computing dimensions of varieties of characters of 2-orbifolds, including the Hitchin component. The author applies this computation to the dimension growth of varieties of characters of some 3-dimensional manifolds in \(\mathrm{SL}_n(\mathbb{C})\).