Small genus-4 Lefschetz fibrations on simply-connected 4-manifolds

Altunoz T.

TURKISH JOURNAL OF MATHEMATICS, cilt.46, sa.4, ss.1268-1290, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3906/mat-2108-85
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1268-1290
  • Anahtar Kelimeler: Symplectic 4-manifolds, mapping class groups, Lefschetz fibrations, exotic manifolds, SINGULAR FIBERS, MINIMAL NUMBER, SMOOTH STRUCTURES, SIGNATURE
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We consider simply connected 4-manifolds admitting Lefschetz fibrations over the 2-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus 4 on simply-connected 4-manifolds which are exotic symplectic 4-manifolds in the homeomorphism classes of CP2 #8<(CP2)over bar> and CP2#9<(CP2)over bar>, respectively. From these, we provide upper bounds for the minimal number of singular fibers of such fibrations. In addition, we prove that this number is equal to 18 for g = 3 when such fibrations are hyperelliptic. Moreover, we discuss these numbers for higher genera.