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Sections Of Surface Bundles And Lefschetz Fibrations, Inanc Baykur, Mustafa Korkmaz, Naoyuki Monden
Sections Of Surface Bundles And Lefschetz Fibrations, Inanc Baykur, Mustafa Korkmaz, Naoyuki Monden
Inanc Baykur
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 …