Algebraic & Geometric Topology

On high-dimensional representations of knot groups

Stefan Friedl and Michael Heusener

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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.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 1 (2018), 313-332.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1517454218

Digital Object Identifier
doi:10.2140/agt.2018.18.313

Mathematical Reviews number (MathSciNet)
MR3748245

Zentralblatt MATH identifier
1383.57004

Subjects
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

Keywords
knots character knot groups representations

Citation

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


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