51 citations · 61 across the 13 of their papers we have counts for
7 papers · 1 filter
Geometric structures and representations of knot groups from knot diagrams
Kathleen L. Petersen, Anastasiia Tsvietkova
We describe a new method of producing equations for the canonical component of representation variety of a knot group into . Unlike known methods, this one does…
Small representations of Seifert fiber space groups
Neil R Hoffman, Kathleen L Petersen
Let be a Seifert fiber space with non-abelian fundamental group and admitting a triangulation with tetrahedra. We show that there is a non-abelian $\text{PSL}(2, \mathbb{F}…
Symmetries and Detection of Surfaces by the Character Variety
Jay Leach, Kathleen Petersen
We extend Culler and Shalen's construction of detecting essential surfaces in 3-manifolds to 3-orbifolds. We do so in the setting of the character varie…
Character varieties of double twist links
Kathleen L. Petersen, Anh T. Tran
We compute both natural and smooth models for the character varieties of the two component double twist links, an infinite family of two-bridge links indexed as $…
Gonality and genus of canonical components of character varieties
Kathleen L. Petersen, Alan W. Reid
Let M be a two cusped hyperbolic 3-manifold and let M(r) be the result of r Dehn filling of a fixed cusp of M. We study canonical components of the SL(2,C) character varieties of M…
Character varieties of once-punctured torus bundles with tunnel number one
Kenneth L. Baker, Kathleen L. Petersen
We determine the PSL_2(C) and SL_2(C) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling…
On Character varieties of two-bridge knot groups
Melissa L. Macasieb, Kathleen L. Petersen, Ronald M. van Luijk
We find explicit models for the PSL(2,C)- and SL(2,C)-character varieties of the fundamental groups of complements in S^3 of an infinite family of two-bridge knots that contains th…