A Lefschetz fibration is a smooth 4-manifold object admitting surface bundle structure over surface except finite singular fibers, whose singularity is only nodal type.

From the structure of singular fiber, each monodromy of a singular fiber is given by a right handed Dehn twist along a curve, called a vanishing cycle, in the fiber surface.

Collecting all monodromy data from singular fibers, we have a monodromy factorization into right handed Dehn twists, which is the complete information of the Lefschetz fibration.

In my thesis paper, I construct a fibration with one singular fiber which has a periodic monodromy (that is, monodromy homeomorphism is isotopic to a periodic map).

From the idea of Matsumoto, I give a splitting of the singular fiber into Lefschetz fibers and their vanishing cycles for some collection of periodic monodromies.

In this talk, I explain the detailed story of reading vanishing cycles using two branched cover structure of fibers.