Let $p$ be a finite regular covering on a 2-sphere with at least three branch points. In this paper, we construct a local signature for the class of fibered 4-manifolds whose general fibers are isomorphic to the covering $p$.
"A local signature for fibered 4-manifolds with a finite group action." Tohoku Math. J. (2) 65 (4) 545 - 568, 2013. https://doi.org/10.2748/tmj/1386354295