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 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.

61 pages, 39 figures; added details to several proofs. Version published by Algebr. Geom. Topol. 10 (2010), 465--524

References in corpus (4)

• Lectures on open book decompositions and contact structures
• Heegaard Floer homologies and contact structures
• Surgery diagrams for contact 3-manifolds
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds

Cited by in corpus (9)

• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• A contact invariant in sutured monopole homology
• Sutured Floer homology and invariants of Legendrian and transverse knots
• Monopole Floer homology and Legendrian knots
• Ozsváth-Szabó invariants of contact surgeries
• Symmetries and adjunction inequalities for knot Floer homology
• On contact surgery and knot Floer invariants
• Whitney polygons, symbol homology and cobordism maps
• Holomorphic discs and surgery exact triangles