Volume 17, issue 4 (2017)

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Eigenvalue varieties of Brunnian links

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 ${\mathbb{S}}^{3}$.

Keywords
knot, link, A-polynomial, eigenvalue variety
Primary: 57M25
Secondary: 57M27
Publication
Received: 11 December 2015
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