Lefschetz Fibrations on Knot Surgery 4-Manifolds Via Stallings Twist

In this paper, we construct a family of simply connected minimal symplectic 4-manifolds that admit arbitrarily many nonisomorphic Lefschetz fibration structures with the same genus fiber. We obtain these families by performing knot surgery on an elliptic surface E(2) using connected sums of n copies of fibered knots, which in turn are obtained by Stallings twist from the square knot. Thus, all of these 4 -manifolds are homotopy E (2) surfaces. We show that they admit 2(n) mutually nonisomorphic Lefschetz fibration structures of fiber genus (4n + 1) by comparing their monodromy groups that are induced from the corresponding monodromy factorizations.