Luttinger surgery is a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold. The surgery was introduced by Karl Murad Luttinger in 1995, who used it to study Lagrangian tori in R^4. Luttinger's surgery has been a very effective tool recently for constructing exotic smooth structures on various 4-manifolds. In this talk, using Luttinger surgery, I will construct an infinite family of exotic Lefschetz fibrations over 2-sphere whose total space has arbitrary finitely presented group G as the fundamental group. If time permits, I will also construct infinitely many exotic Stein fillings with the fundamental group G
This is a joint work with Burak Ozbagci (Koc University, Turkey).