Lefschetz Fibrations on 4-manifolds

Korkmaz, Mustafa
Stipsicz, Andras
We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces for , and to for . 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 , with one possible exception when . 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 and from small Lefschetz fibrations over surfaces of higher genera.
Citation Formats
M. Korkmaz and A. Stipsicz, Lefschetz Fibrations on 4-manifolds. 2009, p. 296.