Dehn twists in Heegaard Floer homology

Abstract

We derive a new exact sequence in the hat-version of Heegaard Floer homology. As a consequence we see a functorial connection between the invariant of Legendrian knots L̂ and the contact element. As an application we derive two vanishing results of the contact element making it possible to easily read off its vanishing out of a surgery presentation in suitable situations.