Contact Dehn Surgery

Now we are in the position to describe the contact version of the smooth surgery scheme we started our notes with. This method provides a rich and yet to be explored source of all kinds of contact 3-manifolds. The approach to 3-dimensional contact topology we outline here was initiated by Ding and Geiges [16, 17], see also [18, 19]. Using contact surgery diagrams — and applying achiral Lefschetz fibrations — we will make connection to Giroux’s theory on open book decompositions, and we will also show a way to determine homotopic properties of the contact structures under examination. We begin by reviewing the classification of tight structures on Sl × D2 due to Honda — this is the result which allows us to define contact surgery diagrams.