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

Altunoz T.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.18, sa.3, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00009-021-01750-4
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.