SECTIONS OF SURFACE BUNDLES AND LEFSCHETZ FIBRATIONS

Date

2013-11-01

Author

Baykur, R. Inanc
Korkmaz, Mustafa
Monden, Naoyuki

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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.

URI

https://hdl.handle.net/11511/48554

Collections

Department of Mathematics, Article