%0 Journal Article
%T Sections of surface bundles and Lefschetz fibrations
%A R. Inanc Baykur
%A Mustafa Korkmaz
%A Naoyuki Monden
%J Mathematics
%D 2011
%I arXiv
%X We investigate the possible self-intersection numbers for sections of surface bundles and Lefschetz fibrations over surfaces. When the fiber genus g and the base genus h are positive, we prove that the adjunction bound 2h-2 is the only universal bound on the self-intersection number of a section of any such genus g bundle and fibration. As a side result, in the mapping class group of a surface with boundary, we calculate the precise value of the commutator lengths of all powers of a Dehn twist about a boundary component, concluding that the stable commutator length of such a Dehn twist is 1/2. We furthermore prove that there is no upper bound on the number of critical points of genus-g Lefschetz fibrations over surfaces with positive genera admitting sections of maximal self-intersection, for g at least two.
%U http://arxiv.org/abs/1110.1224v3