Reeb periodic orbits after a bypass attachment

Abstract

On a 3-dimensional contact manifold with boundary, a bypass attachment is an elementary change of the contact structure consisting in the attachment of a thickened half-disc with a prescribed contact structure along an arc on the boundary. We give a model bypass attachment in which we describe the periodic orbits of the Reeb vector field created by the bypass attachment in terms of Reeb chords of the attachment arc. As an application, we compute the contact homology of a product neighbourhood of a convex surface after a bypass attachment, and the contact homology of some contact structures on solid tori.

References in corpus (6)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• Sutures and contact homology I
• Polyfolds And A General Fredholm Theory
• Embedded contact homology and Seiberg-Witten Floer cohomology I
• HF = ECH via open book decompositions: a summary
• The cylindrical contact homology of universally tight sutured contact solid tori