Communications in Analysis and Geometry
Volume 13 (2005)
Surface bundles versus Heegaard splittings
Pages: 903 – 928
This paper studies Heegaard splittings of surface bundles via the curve complex of the fibre. The translation distance of the monodromy is the smallest distance it moves any vertex of the curve complex. We prove that the translation distance is bounded above in terms of the genus of any strongly irreducible Heegaard splitting. As a consequence, if a splitting surface has small genus compared to the translation distance of the monodromy, then the splitting is standard.