Using the Jones Polynomial to Prove Infinite Families of Knots Satisfy the Cosmetic Surgery Conjecture

TL;DR

This paper demonstrates that two infinite families of knots satisfy the Cosmetic Surgery Conjecture by computing their Jones polynomials and related invariants, extending methods for both computation and family generation.

Contribution

It introduces a novel approach using Jones polynomial invariants to verify the Cosmetic Surgery Conjecture for infinite knot families.

Findings

Both knot families satisfy the conjecture.

Extended methods for computing Jones polynomials.

Extended methods for generating knot families.

Abstract

This paper computes the Jones polynomial and the invariants obstructing cosmetic surgery which are derived from it for two infinite families of knots, proving they satisfy the Purely Cosmetic Surgery Conjecture. Both the method of computation and the method for generating families of knots extend.