Lefschetz fibration structures on knot surgery 4-manifolds

TL;DR

This paper investigates Lefschetz fibration structures on knot surgery 4-manifolds derived from elliptic surfaces using Kanenobu knots, revealing infinite families of simply connected, mutually diffeomorphic, and symplectic 4-manifolds with multiple Lefschetz fibrations.

Contribution

It constructs infinite families of 4-manifolds with multiple Lefschetz fibrations and explores their diffeomorphism and symplectic properties, advancing understanding of Lefschetz structures in knot surgery.

Findings

Infinite families of simply connected, mutually diffeomorphic 4-manifolds.

Existence of multiple inequivalent Lefschetz fibrations on the same 4-manifold.

Construction of symplectic 4-manifolds with multiple Lefschetz fibrations.

Abstract

In this article we study Lefschetz fibration structures on knot surgery 4-manifolds obtained from an elliptic surface E(2) using Kanenobu knots $K$. As a result, we get an infinite family of simply connected mutually diffeomorphic 4-manifolds coming from a pair of inequivalent Kanenobu knots. We also obtain an infinite family of simply connected symplectic 4-manifolds, each of which admits more than one inequivalent Lefschetz fibration structures of the same generic fiber.