SECTIONS OF SURFACE BUNDLES AND LEFSCHETZ FIBRATIONS


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Baykur R. I. , KORKMAZ M. , Monden N.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.365, ss.5999-6016, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 365 Konu: 11
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1090/s0002-9947-2013-05840-0
  • Dergi Adı: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.5999-6016

Özet

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.