c.f. [@Gabai5 Theorem 8.8], [@kazezroberts Theorem 4.4], [@Roberts2001b].

Surface homeomorphisms of the sort we consider arise naturally as monodromies of fibered knots in 3-manifolds or, equivalently, open book decompositions of 3-manifolds with connected binding. Indeed, if $K\subset Y$ is a fibered knot then the complement of a neighborhood of $K$ is a bundle over $S^1$ with fiber a compact surface $S$ with one boundary component. This bundle is described by a monodromy homeomorphism $\phi_K: S\rightarrow S$ that is the identity on the boundary and well-defined up to isotopy and conjugation. Hence we can think of the twist coefficient as giving rise to an invariant of fibered knots in 3-manifolds, $K \mapsto \tau(\phi_K)$, where we suppress the choice of fibration from our notation. Our main result shows that if the 3-manifold is fixed, then there is an [*a priori*]{} bound on the value of the twist coefficient for any fibered knot in that manifold.

\[thm1\] Let $Y$ be a closed oriented 3-manifold. Then there exists an integer $N_Y\geq 0$ with the following property: Let $K$ be any fibered knot in $Y$ and let $\phi_K$ denote its monodromy. Then $$|\tau(\phi_K)| \leq N_Y + 1.$$

In the case that a knot fibers in 