The existence of an indecomposable minimal genus two Lefschetz fibration

Abstract

It was shown by Usher that any fiber sum of Lefschetz fibrations over $S^2$ is minimal, which was conjectured by Stipsicz. We prove that the converse does not hold by showing that there exists an indecomposable minimal genus-2 Lefschetz fibration.

7 pages, some comments and references were added

References in corpus (2)

• Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds
• Genus two Lefschetz fibrations with $b_2^{+}=1$ and ${c_1}^2=1,2$