Orientation double covers of non-orientable Lefschetz fibrations

Abstract

In this paper, we prove that the composition of the standard orientation double covering map and a non-orientable Lefschetz fibration is an achiral Lefschetz fibration and specify a monodromy factorization of this composition. As an application of these results, we also give three transformations with respect to monodromy factorizations of non-orientable Lefschetz fibrations which do not change their isomorphism classes via the similar result to orientable Lefschetz fibrations.