Local signature defect of fibered complex surfaces via monodromy and stable reduction

Abstract

We consider the localization problem of signature of a fibered complex surface. In this paper, we analyze the contribution of topological monodromy to the local signature of a fiber germ. In order to realize it, we describe explicitly the behavior of Atiyah–Patodi–Singer’s eta invariant under the stable reduction of a fiber germ in terms of Nielsen’s data.