Volume 17, issue 4 (2017)

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Eigenvalue varieties of Brunnian links

François Malabre

Algebraic & Geometric Topology 17 (2017) 2039–2050

In this article, it is proved that the eigenvalue variety of the exterior of a nontrivial, non-Hopf, Brunnian link in S3 contains a nontrivial component of maximal dimension. Eigenvalue varieties were first introduced to generalize the A–polynomial of knots in S3 to manifolds with nonconnected toric boundary. The result presented here generalizes, for Brunnian links, the nontriviality of the A–polynomial of nontrivial knots in S3.

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knot, link, A-polynomial, eigenvalue variety
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27
Received: 11 December 2015
Revised: 29 November 2016
Accepted: 13 December 2016
Published: 3 August 2017
François Malabre
Department of Mathematics
University of Barcelona
Gran Vía, 585
08007 Barcelona