Twisted Alexander Polynomials and Fibered Classes in Ribbon Homology Cobordisms

Abstract

Let $Y_-$ and $Y_+$ be two compact 3-manifolds with empty or toroidal boundary. A 4-dimensional ribbon homology cobordism is a homologically trivial cobordism built with 1-handles and 2-handles. In this note, following the work of Friedl and collaborators, we apply twisted Alexander polynomials to show that the fibered classes of $Y_+$ map to those of $Y_-$.