Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations
  We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S^2. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore, these examples show that fiber sums of holomorphic Lefschetz fibrations do not necessarily admit complex structures. 
Burak Ozbagci and Andr\'as I. Stipsicz