2002/12/06 by David Bachman, Bachman, David, Saul Schleimer +1
Mathematics · #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M99
paper · pdf · doi:10.48550/arxiv.math/0212104
22 pages, 5 figures
arxiv created 2002/12/06 · arxiv updated 2009/11/30
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, the splitting is standard.