On lassos and the Jones polynomial of satellite knots

الأصل · EN

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 Δₖ(t), I then use these lassos as patterns to construct families of satellite knots that have Alexander polynomial Δₖ(tᵈ) where d∪ {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.