A Lefschetz fibration on minimal symplectic fillings of a quotient surface singularity

Abstract

In this article, we construct a genus-0 or genus-1 positive allowable Lefschetz fibration on any minimal symplectic filling of the link of non-cyclic quotient surface singularities. As a byproduct, we also show that any minimal symplectic filling of the link of quotient surface singularities can be obtained from a sequence of rational blowdowns from its minimal resolution.