Minimal number of singular fibers in a Lefschetz fibration
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.129, sa.5, ss.1545-1549, 2001 (SCI-Expanded, Scopus)
- 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
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- 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.