Open book decompositions of fiber sums in contact topology

Abstract

We describe compatible open books for the fiber connected sum along binding components and along multisections of open books. As an application, the first description provides simple ways of constructing open books supporting all tight contact structures on $T^3$, recovering a result by Van Horn-Morris, as well as an open book supporting the result of a Lutz twist along a binding component of an open book, recovering a result by Ozbagci and Pamuk.