Sections of surface bundles and lefschetz fibrations

R. Inanç Baykur, Mustafa Korkmaz, Naoyuki Monden

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)5999-6016
Number of pages18
JournalTransactions of the American Mathematical Society
Volume365
Issue number11
DOIs
Publication statusPublished - Aug 27 2013
Externally publishedYes

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Lefschetz Fibration
Bundle
Genus
Self-intersection
Electric commutators
Dehn Twist
Intersection number
Commutator
Universal Bounds
Adjunction
Mapping Class Group
Fibration
Critical point
Fibers
Fiber
Upper bound
Calculate

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Sections of surface bundles and lefschetz fibrations. / Baykur, R. Inanç; Korkmaz, Mustafa; Monden, Naoyuki.

In: Transactions of the American Mathematical Society, Vol. 365, No. 11, 27.08.2013, p. 5999-6016.

Research output: Contribution to journalArticle

Baykur, R. Inanç ; Korkmaz, Mustafa ; Monden, Naoyuki. / Sections of surface bundles and lefschetz fibrations. In: Transactions of the American Mathematical Society. 2013 ; Vol. 365, No. 11. pp. 5999-6016.
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