Homology handles with trivial Alexander polynomial

TL;DR

This paper demonstrates that certain 3-dimensional homology handles with trivial Alexander polynomial bound specific 4-manifolds and are topologically null cobordant, extending understanding of their topological properties.

Contribution

It establishes that homology handles with trivial Alexander polynomial bound homology $S^1\times D^3$ and are topologically null $\widetilde{H}$-cobordant, using Freedman and Quinn's results.

Findings

Homology handles with trivial Alexander polynomial bound homology $S^1\times D^3$.

Such handles are topologically null $\widetilde{H}$-cobordant.

Extension of Freedman and Quinn's results to homology handles.

Abstract

Using Freedman and Quinn's result for $\mathbb{Z}$-homology 3-spheres, we show that a 3-dimensional homology handle with trivial Alexander polynomial bounds a homology $S^1\times D^3$. As a consequence, a distinguished homology handle with trivial Alexander polynomial is topologically null $\widetilde{H}$-cobordant.