Surgery diagrams and open book decomposisions of contact 3-manifolds (Q2568509)

For a contact 3-manifold \((Y,\xi)\) given by contact \((\pm 1)\)-surgery, a compatible open book decomposition is constructed in an algorithmic way. This is done by reading the surgery data as a Kirby diagram describing a 4-manifold \(X\) with \(\partial X = Y\) and constructing an achiral Lefschetz fibration \(X \to D^2\), which induces the desired open book decomposition. As a corollary, it is shown that the open book decomposition can be chosen so that its monodromy is a product of Dehn twists at most one of which is left-handed. Applications to the computation of homotopy invariants of contact structures are presented.