Non-loose torus knots in $S^1\times S^2$

TL;DR

This paper provides a comprehensive classification of non-loose Legendrian and transverse torus knots in all contact structures on the manifold S^1×S^2, advancing understanding of knot theory in contact topology.

Contribution

It offers the first complete coarse classification of non-loose Legendrian and transverse torus knots in S^1×S^2 across all contact structures.

Findings

Classification of non-loose Legendrian torus knots

Classification of non-loose transverse torus knots

Applicable to all contact structures on S^1×S^2

Abstract

In this paper, we present a complete coarse classification of non-loose Legendrian and transverse torus knots in any contact structure on $S^1\times S^2$.