Lefschetz fibrations on knot surgery $4$-manifolds via Stallings twist

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 $3_1♯3_1^{\ast }$. By comparing their monodromy groups induced from the corresponding monodromy factorizations, we show that they admit mutually nonisomorphic Lefschetz fibration structures.

16 pages, 5 figures

References in corpus (1)

• Positive Dehn Twist Expressions for some New Involutions in the Mapping Class Group II

Cited by in corpus (1)

• Bilinear-form invariants of Lefschetz fibrations over the 2-sphere