Algebraic & Geometric Topology

On high-dimensional representations of knot groups

Stefan Friedl and Michael Heusener

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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 , ) –character variety. A component of the SL ( n , ) –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 , ) –character variety. We show that given any nontrivial knot K and sufficiently large n the SL ( n , ) –character variety of K admits high-dimensional components.

Article information

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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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds
Secondary: 57M50: Geometric structures on low-dimensional manifolds

knots character knot groups representations


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.

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