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Unpublished Paper
Sections of Surface Bundles and Lefschetz Fibrations
Transactions of the American Mathematical Society (2013)
  • Inanc Baykur, University of Massachusetts - Amherst
  • Mustafa Korkmaz
  • Naoyuki Monden
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 ≥ 2.
Publication Date
August 2, 2013
Prepublished version downloaded from ArXiv. Published version is located at
Citation Information
Inanc Baykur, Mustafa Korkmaz and Naoyuki Monden. "Sections of Surface Bundles and Lefschetz Fibrations" Transactions of the American Mathematical Society (2013)
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