The existence of an indecomposable minimal genus two Lefschetz fibration

Anar Akhmedov, Naoyuki Monden

Published 2018-09-25Version 1

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.