On high-dimensional representations of knot groups

Friedl, Stefan; Heusener, Michael

doi:10.2140/agt.2018.18.313

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

On high-dimensional representations of knot groups

Stefan Friedl and Michael Heusener

Algebraic & Geometric Topology 18 (2018) 313–332

DOI: 10.2140/agt.2018.18.313

Abstract

Given a hyperbolic knot $K$ and any $n \geq 2$ the abelian representations and the holonomy representation each give rise to an $(n - 1)$ –dimensional component in the $SL (n, ℂ)$ –character variety. A component of the $SL (n, ℂ)$ –character variety of dimension $\geq n$ is called high-dimensional.

It was proved by D Cooper and D Long that there exist hyperbolic knots with high-dimensional components in the $SL (2, ℂ)$ –character variety. We show that given any nontrivial knot $K$ and sufficiently large $n$ the $SL (n, ℂ)$ –character variety of $K$ admits high-dimensional components.

PDF Access Denied

We have not been able to recognize your IP address 3.239.2.192 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

knots, character, knot groups, representations

Mathematical Subject Classification 2010

Primary: 57M25, 57M27

Secondary: 57M50

References

Publication

Received: 14 October 2016

Revised: 4 April 2017

Accepted: 15 July 2017

Published: 10 January 2018

Authors

Stefan Friedl
Fakultät für Mathematik Universität Regensburg Regensburg Germany

Michael Heusener
Laboratoire de Mathématiques Blaise Pascal - UMR 6620 - CNRS Université Clermont Auvergne Campus des Cézeaux Aubière France
http://math.univ-bpclermont.fr/~heusener/

Volume 18, issue 1 (2018)