Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 18, Number 1 (2018), 313-332.
On high-dimensional representations of knot groups
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.
Algebr. Geom. Topol., Volume 18, Number 1 (2018), 313-332.
Received: 14 October 2016
Revised: 4 April 2017
Accepted: 15 July 2017
First available in Project Euclid: 1 February 2018
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Friedl, Stefan; Heusener, Michael. On high-dimensional representations of knot groups. Algebr. Geom. Topol. 18 (2018), no. 1, 313--332. doi:10.2140/agt.2018.18.313. https://projecteuclid.org/euclid.agt/1517454218