Abstract
Given a hyperbolic knot K and any n >= 2 the abelian representations and the holonomy representation each give rise to an (n-1)-dimensional component in the SL (n, C)-character variety. A component of the SL (n, C)-character variety of dimension >= n is called high-dimensional. It was proved by D Cooper and D Long that there exist hyperbolic knots with high-dimensional components in the SL (2, ...
Abstract
Given a hyperbolic knot K and any n >= 2 the abelian representations and the holonomy representation each give rise to an (n-1)-dimensional component in the SL (n, C)-character variety. A component of the SL (n, C)-character variety of dimension >= n is called high-dimensional. It was proved by D Cooper and D Long that there exist hyperbolic knots with high-dimensional components in the SL (2, C)-character variety. We show that given any nontrivial knot K and sufficiently large n the SL (n, C)-character variety of K admits high-dimensional components.
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