On lassos and the Jones polynomial of satellite knots
Abstract
In this master thesis, I present a new family of knots in the solid torus called lassos, and their properties. Given a knot K with Alexander polynomial K(t), I then use these lassos as patterns to construct families of satellite knots that have Alexander polynomial K(td) where d∈N \0\. In particular, I prove that if d∈\0,1,2,3\ these satellite knots have different Jones polynomials. For this purpose, I give rise to a formula for calculating the Jones polynomial of a satellite knot in terms of the Jones polynomials of its pattern and companion.
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