A local signature for fibrations with a finite group action

TL;DR

This paper introduces a local signature invariant for a class of fibrations over a 2-sphere, where the fibers are finite regular coverings with group actions, providing new tools for understanding their structure.

Contribution

The paper constructs a local signature for fibrations with fibers as finite regular coverings, extending the understanding of their geometric and topological properties.

Findings

Defined a local signature for these fibrations

Applied the construction to coverings with finite group actions

Enhanced the classification of such fibrations

Abstract

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 fibrations whose general fibers are isomorphic to the covering p.