Volume 18, issue 1 (2018)

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On high-dimensional representations of knot groups

Stefan Friedl and Michael Heusener

Algebraic & Geometric Topology 18 (2018) 313–332

Given a hyperbolic knot K and any n 2 the abelian representations and the holonomy representation each give rise to an (n1)–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.

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knots, character, knot groups, representations
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57M50
Received: 14 October 2016
Revised: 4 April 2017
Accepted: 15 July 2017
Published: 10 January 2018
Stefan Friedl
Fakultät für Mathematik
Universität Regensburg
Michael Heusener
Laboratoire de Mathématiques Blaise Pascal - UMR 6620 - CNRS
Université Clermont Auvergne
Campus des Cézeaux