Small Lefschetz fibrations and exotic 4-manifolds


Creative Commons License

Baykur R. I. , KORKMAZ M.

MATHEMATISCHE ANNALEN, cilt.367, ss.1333-1361, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 367
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s00208-016-1466-2
  • Dergi Adı: MATHEMATISCHE ANNALEN
  • Sayfa Sayıları: ss.1333-1361

Özet

We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces CP2#pCP (CP) over bar (2) for P = 7,8,9, and to 3CP(2)#qCP (CP) over bar (2) for q = 12, . . . , 19. Complementarily, we prove that there are no minimal genus-2 Lefschetz fibrations whose total spaces are homeomorphic to any other simply-connected 4-manifold with b(+) <= 3, with one possible exception when b(+) = 3. Meanwhile, we produce positive Dehn twist factorizations for several new genus-2 Lefschetz fibrations with small number of critical points, including the smallest possible example, which follow from a reverse engineering procedure we introduce for this setting. We also derive exotic minimal symplectic 4-manifolds in the homeomorphism classes of CP2#4CP (CP) over bar (2) and 3CP(2)#6CP (CP) over bar (2) from small Lefschetz fibrations over surfaces of higher genera.