On lassos and the Jones polynomial of satellite knots

Adrián Jiménez Pascual

Published 2015-01-08Version 1

The purpose of this paper is to present in the first part of it a family of knots in the solid torus called \emph{lassos}, and their properties. The second part will be devoted to analyze the Kauffman bracket and Jones polynomial of satellite knots (explicit formulae for their calculus will be given). In the last section we will use all the concepts defined and discussed in this paper to explicitly construct families of knots with the same Alexander polynomial but different Jones polynomial