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2018 On high-dimensional representations of knot groups
Stefan Friedl, Michael Heusener
Algebr. Geom. Topol. 18(1): 313-332 (2018). DOI: 10.2140/agt.2018.18.313

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 , ) –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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Stefan Friedl. Michael Heusener. "On high-dimensional representations of knot groups." Algebr. Geom. Topol. 18 (1) 313 - 332, 2018. https://doi.org/10.2140/agt.2018.18.313

Information

Received: 14 October 2016; Revised: 4 April 2017; Accepted: 15 July 2017; Published: 2018
First available in Project Euclid: 1 February 2018

zbMATH: 1383.57004
MathSciNet: MR3748245
Digital Object Identifier: 10.2140/agt.2018.18.313

Subjects:
Primary: 57M25, 57M27
Secondary: 57M50

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 1 • 2018
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