Title: The Dimension of the Restricted Hitchin Component for a Triangle Group
Speaker: Elise Weir, The University of Tennessee at Knoxville
Abstract: A triangle group T(p,q,r) is the group of rotational symmetries of a tiling of the hyperbolic plane by geodesic triangles. We will begin by discussing a component of the representation variety of T(p,q,r) in PSL(n,R) called the Hitchin component, noteworthy in part because representations inside are all discrete and faithful.
For n = 3, the dimension of the Hitchin component for hyperbolic triangle groups follows from a special case of work by Choi and Goldman. More recently, Long and Thistlethwaite determined its dimension for general n >=3. Our results retain this broader n-dimensional context, but focus in on those representations contained in the subgroup G = SO(m,m+1) or G = Sp(2m). In particular, we will give a formula for the dimension of this "restricted" Hitchin component for hyperbolic T(p,q,r) within G for all n >=3.
Seminar URL: https://research.math.osu.edu/topology/
