Minimal number of singular fibers in a Lefschetz fibration

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Korkmaz M., Ozbagci B.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.129, no.5, pp.1545-1549, 2001 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 129 Issue: 5
  • Publication Date: 2001
  • Doi Number: 10.1090/s0002-9939-00-05676-8
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1545-1549
  • Keywords: Lefschetz fibrations, 4-manifolds, mapping class groups
  • Middle East Technical University Affiliated: Yes

Abstract

There exists a (relatively minimal) genus g Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus h iff g greater than or equal to 3 and h greater than or equal to 2. The singular fiber can be chosen to be reducible or irreducible. Other results are that every Dehn twist on a closed surface of genus at least three is a product of two commutators and no Dehn twist on any closed surface is equal to a single commutator.