This research demonstrates monodromy factorization in non-orientable Lefschetz fibrations, implying transformations do not alter isomorphism classes.
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.
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T. Yoshikawa (2025) studied this question.
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