Constructing lefschetz fibrations via cyclic group actions i

This article is first of two part series studying the Lefschetz fibrations over S² using the cyclic group actions. In this article, using various cyclic group actions on product symplectic 4-manifolds T² ×T² and ∑² × ∑²and applying the resolutions of cyclic quotient singularities, we study the monodromies of genus one and genus two Lefschetz _brations over S². The second article in this series will be devoted to the study of the monodromies of genus three Lefschetz fibrations over S² and some constructions of new Lefschetz fibrations using the rational blow-down surgery.