Minimal number of singular fibers in a Lefschetz fibration

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Korkmaz M., Ozbagci B.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.129, sa.5, ss.1545-1549, 2001 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 129 Sayı: 5
  • Basım Tarihi: 2001
  • Doi Numarası: 10.1090/s0002-9939-00-05676-8
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1545-1549
  • Anahtar Kelimeler: Lefschetz fibrations, 4-manifolds, mapping class groups
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.