#### Volume 17, issue 4 (2017)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747

### François Malabre

Algebraic & Geometric Topology 17 (2017) 2039–2050
##### Abstract

In this article, it is proved that the eigenvalue variety of the exterior of a nontrivial, non-Hopf, Brunnian link in ${\mathbb{S}}^{3}$ contains a nontrivial component of maximal dimension. Eigenvalue varieties were first introduced to generalize the $A$–polynomial of knots in ${\mathbb{S}}^{3}$ to manifolds with nonconnected toric boundary. The result presented here generalizes, for Brunnian links, the nontriviality of the $A$–polynomial of nontrivial knots in ${\mathbb{S}}^{3}$.

Primary: 57M25
Secondary: 57M27
##### Publication
Revised: 29 November 2016
Accepted: 13 December 2016
Published: 3 August 2017
##### Authors
 François Malabre Department of Mathematics University of Barcelona Gran Vía, 585 08007 Barcelona Spain