A criterion for the Legendrian simplicity of the connected sum

TL;DR

This paper establishes criteria to determine when the connected sum of knots in three-dimensional space results in a Legendrian simple knot, advancing understanding in contact topology.

Contribution

It provides the first complete characterization of Legendrian simplicity for connected sums of knots, filling a key gap in contact topology theory.

Findings

Necessary and sufficient conditions for Legendrian simplicity of connected sums

Characterization of Legendrian invariants under connected sum

Extension of Legendrian knot classification methods

Abstract

In this paper, we provide the necessary and sufficient conditions for the connected sum of knots in $S^3$ to be Legendrian simple.