Let be a
contact 3–manifold. We present two new algorithms, the first of which converts an open
book
supporting
with connected binding into a contact surgery diagram. The second turns a contact surgery
diagram for
into a supporting open book decomposition. These constructions
lead to a refinement of a result of Ding and Geiges [Math. Proc.
Cambridge Philos. Soc. 136 (2004) 583–598], which states that every such
may be obtained by
contact surgery from ,
as well as bounds on the support norm and genus (Etnyre and Ozbagci [Trans.
Amer. Math. Soc. 360 (2008) 3133–3151]) of contact manifolds obtained
by surgery in terms of classical link data. We then introduce Kirby moves
called ribbon moves, which use mapping class relations to modify contact
surgery diagrams. Any two surgery diagrams of the same contact 3–manifold
are related by a sequence of Legendrian isotopies and ribbon moves. As
most of our results are computational in nature, a number of examples are
analyzed.
