OPEN BOOKS AND EXACT SYMPLECTIC COBORDISMS

Abstract. Given two open books with equal pages we show the existence of an exact symplectic cobordism whose negative end equals the disjoint union of the contact manifolds associated to the given open books, and whose positive end induces the contact manifold associated to the open book with the same page and monodromy given by the concatenation of the given ones. Following an outline by Wendl we show that the complement of the binding of an open book cannot contain any local filling obstruction. Given a contact 3-manifold, according to Eliashberg, there is a symplectic cobordism to a fibration over the circle with symplectic fibres. We extend this result to higher dimensions recovering a result by Dörner–Geiges–Zehmisch. Our cobordisms can also be thought of as the result of the attachment of a generalised symplectic 1-handle