Genus-3 Lefschetz Fibrations and Exotic 4-Manifolds with b(2)(+)=3

Altunoz T.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.18, no.3, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1007/s00009-021-01750-4
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Middle East Technical University Affiliated: Yes

Abstract

We explicitly construct a genus-3 Lefschetz fibration over S-2, whose total space is T-2 x S-2 #6 (CP2) over bar using the monodromy of Matsumoto's genus-2 Lefschetz fibration. We then construct more genus-3 Lefschetz fibrations, whose total spaces are exotic minimal symplectic 4-manifolds 3CP(2)#q (CP2) over bar for q = 13,..., 19. We also generalize our construction to get genus-3k Lefschetz fibration structure on the 4-manifold Sigma(k) x S-2 #6 (CP2) over bar using the generalized Matsumoto's genus-2k Lefschetz fibration. From this generalized version, we derive further exotic 4-manifolds via Luttinger surgery and twisted fiber sum.