Twisted Alexander Polynomials and Fibered Classes in Ribbon Homology Cobordisms

TL;DR

This paper explores how twisted Alexander polynomials can be used to understand the relationship between fibered classes in 3-manifolds connected by ribbon homology cobordisms, extending previous work in the field.

Contribution

It demonstrates that fibered classes are preserved under the induced maps in ribbon homology cobordisms using twisted Alexander polynomials.

Findings

Fibered classes of Y+ map to those of Y- in ribbon homology cobordisms.

Application of twisted Alexander polynomials to analyze fibered classes.

Extends Friedl's work on fibered classes and 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 $Y_-$.