A signature formula for hyperelliptic broken Lefschetz fibrations

Hyperelliptic broken Lefschetz fibrations are generalizations of hyperelliptic Lefschetz fibrations. We generalize Endo's local signature formula to hyperelliptic directed broken Lefschetz fibrations. This is described in terms of Endo's local signature formula and a rational-valued homomorphism on the subgroup of the hyperelliptic mapping class group of a surface which preserves a simple closed curve setwise.