Comparing invariants of Legendrian knots

Abstract

We prove the equivalence of the invariants EH$(L)$ and ${\mathcal{L}}^{–}(\pm L)$ for oriented Legendrian knots $L$ in the 3-sphere equipped with the standard contact structure, partially extending a previous result by Stipsicz and Vértesi. In the course of the proof we relate the sutured Floer homology groups associated with a knot complement $S^3\setminus K$ and the knot Floer homology of $(S^3,K)$ and define intermediate Legendrian invariants.