On a generalized Jones conjecture

TL;DR

This paper proves a generalized version of the Jones conjecture, establishing that the exponent sum in a minimal braid representation is a knot invariant, using contact geometry techniques.

Contribution

It introduces a generalized form of the Jones conjecture and proves it through contact geometric methods, advancing understanding in knot theory.

Findings

The exponent sum in minimal braid representations is a knot invariant.

The generalized Jones conjecture is proven.

Contact geometry is effective in knot invariant studies.

Abstract

We solve the Jones conjecture, which states that the exponent sum in a minimal braid representation of a knot in S^3 is a knot invariant, by proving a generalized version of the original one. We apply contact geometry to study this problem in knot theory.