Minimality and fiber sum decompositions of Lefschetz fibrations

R. Inanc Baykur

Published 2014-07-21, updated 2015-01-31Version 2

We give a short proof of a conjecture of Stipsicz on the minimality of fiber sums of Lefschetz fibrations, which was proved earlier by Usher. We then construct the first examples of genus g > 1 Lefschetz fibrations on minimal symplectic 4-manifolds which, up to diffeomorphisms of the summands, admit unique decompositions as fiber sums.