Functoriality of the EH class and the LOSS invariant under Lagrangian concordances

TL;DR

This paper demonstrates that certain invariants of Legendrian knots are functorial under Lagrangian concordances, providing new tools to obstruct their existence in Weinstein cobordisms.

Contribution

It establishes the functoriality of the EH class and LOSS invariant under regular Lagrangian concordances, offering computable obstructions.

Findings

EH class and LOSS invariant are functorial under Lagrangian concordances

Provides new obstructions to the existence of regular Lagrangian concordances

Enhances understanding of Legendrian knot invariants in contact topology

Abstract

We show that the EH class and the LOSS invariant of Legendrian knots in contact 3-manifolds are functorial under regular Lagrangian concordances in Weinstein cobordisms. This gives computable obstructions to the existence of regular Lagrangian concordances.