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Unpublished Paper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
Abstract
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.
Disciplines
Publication Date
August 2, 2013
Comments
Prepublished version downloaded from ArXiv. Published version is located at http://www.ams.org/journals/tran/2013-365-11/S0002-9947-2013-05840-0/home.html
Citation Information
Inanc Baykur, Mustafa Korkmaz and Naoyuki Monden. "Sections of Surface Bundles and Lefschetz Fibrations" Transactions of the American Mathematical Society (2013)
Available at: http://works.bepress.com/inanc_baykur/1/