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


Altunoz T.

TURKISH JOURNAL OF MATHEMATICS, vol.46, no.4, pp.1268-1290, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2108-85
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1268-1290
  • Keywords: Symplectic 4-manifolds, mapping class groups, Lefschetz fibrations, exotic manifolds, SINGULAR FIBERS, MINIMAL NUMBER, SMOOTH STRUCTURES, SIGNATURE

Abstract

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.