TL;DR
This paper introduces a new exact sequence in Heegaard Floer homology that links Legendrian knot invariants to contact elements, enabling easier detection of their vanishing through surgery presentations.
Contribution
It presents a novel exact sequence in Heegaard Floer homology and establishes a functorial connection between Legendrian knot invariants and contact elements.
Findings
Derived a new exact sequence in Heegaard Floer homology
Established a functorial link between Legendrian knots and contact elements
Provided criteria for vanishing of contact elements in surgery presentations
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 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.
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