Eigenvalue varieties of Brunnian links

Malabre, François

doi:10.2140/agt.2017.17.2039

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Eigenvalue varieties of Brunnian links

François Malabre

Algebraic & Geometric Topology 17 (2017) 2039–2050

DOI: 10.2140/agt.2017.17.2039

Abstract

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

Keywords

knot, link, A-polynomial, eigenvalue variety

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57M27

References

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

Volume 17, issue 4 (2017)