# Lagrangian cobordisms and Legendrian invariants in knot Floer homology

## TL;DR

This paper studies how Legendrian link invariants in knot Floer homology change under decomposable Lagrangian cobordisms, providing new tools to obstruct their existence.

## Contribution

It establishes functorial properties of LOSS and GRID invariants under certain cobordisms, offering new computable obstructions.

## Key findings

- LOSS and GRID invariants behave functorially under decomposable Lagrangian cobordisms
- New obstructions to the existence of such cobordisms are derived
- Results are effective for computational applications

## Abstract

We prove that the LOSS and GRID invariants of Legendrian links in knot Floer homology behave in certain functorial ways with respect to decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on $\mathbb{R}^3$. Our results give new, computable, and effective obstructions to the existence of such cobordisms.