Doctoral Dissertations

Date of Award


Degree Type


Degree Name

Doctor of Philosophy



Major Professor

Morwen B. Thistlethwaite

Committee Members

Michael W. Berry, Luis R. A. Finotti, Marie Jameson


Given positive integers p, q, r satisfying 1/p + 1/q + 1/r < 1, the hyperbolic triangle group T(p,q,r) is the group of orientation-preserving isometries of a tiling of the hyperbolic plane by triangles congruent to a geodesic triangle with angles π/p, π/q, and π/r. We will examine representations of triangle groups in the Hitchin component, a topologically connected component of the representation variety where representations are always discrete and faithful.We begin by giving a formula for the dimension of a subset of the Hitchin component of an arbitrary hyperbolic triangle T(p, q, r) for general degree n > 2. Depending on whether n is even or odd, we will consider only those Hitchin representations whose images lie in Sp(2m) or SO(m,m + 1), respectively. We call the space of representations satisfying this criterion the restricted Hitchin component.We then provide two new families of representations of the specific triangle group T(3,3,4) into SL(5,R); the image groups of these families are each shown to be Zariski dense in SL(5,R). Further, we consider a restriction to a surface subgroup of finite index in T(3,3,4). For each family, we will demonstrate the existence of a subsequence of representations whose images are pairwise non-conjugate in SL(5,Z) when restricted to a surface subgroup.

Orcid ID

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