PROCEEDINGS OE THE AMERICAN MATHEMATICAL SOCIE1 Volume 72, Number 2, November 1978 OPEN BOOK DECOMPOSITIONS OF 3-MANIFOLDS ROBERT MYERS1 Abstract. We prove that every closed, orientable 3-manifold has an open book decomposition with connected binding. We then give some applications of this result. 1. Introduction. A closed «-manifold has an open book decomposition if it can be constructed as follows: Let F be a compact (n — l)-manifold with 9F ¥=0. Let A be an autohomeomorphism of F which is the identity on 3F. Take F x [0, 1] and identify (A(x), 0) with (x, 1) for x E F and (y, 0) with (y, t) for y EdF,tE [0, 1]. For a manifold Af so constructed let q; F X [0, 1] -> M he the quotient map. q(dF) is called the binding, the q(F X {r}) are called the pages of the decomposition. Alexander [1] proved that every closed orientable 3-manifold has an open book decomposition. It is implied in his paper, and has been widely assumed, that one can always find a decomposition with connected binding. We use a theorem proved independently by Hilden and Montesinos (stated in §2) to prove the following theorem, which was first announced in [13]. Theorem 1. Every closed orientable 3-manifold has an open book decompo- sition with connected binding. This result has been obtained independently, using different techniques, by F. González-Acuña [7]. We work throughout in either the PL or smooth category. Our terminology on braids is consistent with standard usage; we give the book by J. Birman [3] as a reference. For information on branched coverings we refer to R. H. Fox [5]. The author wishes to thank W. Jaco for help in the preparation of this paper for publication. 2. Branched coverings. The following result is widely known. See Alexander [!]• Proposition 1. Let N be a closed 3-manifold having an open book decompo- sition with binding A. Suppose f; M -^> N is a finite sheeted covering space branched over a link L such that L n A =0 and L is transverse to the pages. Presented to the Society, June 20, 1975; received by the editors February 15, 1977 and, in revised form, February 27, 1978. AMS (MOS) subjectclassifications (1970). Primary 57A10;Secondary55A25, 55A10,57D30. Key words and phrases. Open book decomposition, 3-manifold, fibered knot, branched covering space, braid, foliation. 'This research was partially supported by NSF Grant MCS 76-07291. 397 License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use