Given a hyperbolic knot and any the abelian representations and the holonomy representation each give rise to an –dimensional component in the –character variety. A component of the –character variety of dimension is called high-dimensional.
It was proved by D Cooper and D Long that there exist hyperbolic knots with high-dimensional components in the –character variety. We show that given any nontrivial knot and sufficiently large the –character variety of admits high-dimensional components.
"On high-dimensional representations of knot groups." Algebr. Geom. Topol. 18 (1) 313 - 332, 2018. https://doi.org/10.2140/agt.2018.18.313