In this article we construct an infinite family of simply connected minimal symplectic 4-manifolds, each of which admits at least two nonisomorphic Lefschetz fibration structures with the same generic fiber. We obtain such examples by performing knot surgery on an elliptic surface E(n) using a special type of 2-bridge knots.

Abstract. In the article, we study Fintushel-Stern's knot surgery four-manifold E(n) K and its monodromy factorization. For fibered knots we provide a smooth classification of knot surgery 4-manifolds up to twisted fiber sums. We then show that other constructions of 4-manifolds with the same SeibergWitten invariants are in fact diffeomorphic.

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Abstract. We show that the minimal number of singular fibers N (g, 1) in a genus-g Lefschetz fibration over the torus is at least 3. As an application, we show that N (g, 1) ∈ {3, 4} for g ≥ 5, N (g, 1) ∈ {3, 4, 5} for g = 3, 4 and N (2, 1) = 7.

Abstract. In this article we construct a family of knot surgery 4-manifolds admitting arbitrarily many nonisomorphic Lefschetz fibration structures with the same genus fiber. We obtain such families by performing knot surgery on an elliptic surface E(2) using connected sums of fibered knots obtained by Stallings twist from a slice knot 3 1 ♯3 * 1 . By comparing their monodromy groups induced from the corresponding monodromy factorizations, we show that they admit mutually nonisomorphic Lefschetz fibration structures.