Torsion in the homology of Milnor fibers of hyperplane arrangements

TL;DR

This paper explores the presence of torsion in the homology groups of Milnor fibers of complex hyperplane arrangements, revealing new phenomena distinct from the torsion-free nature of their complements.

Contribution

It demonstrates that Milnor fibers can have non-trivial torsion in their homology, contrasting with the torsion-free homology of the arrangement complements.

Findings

Homology groups of Milnor fibers can contain non-trivial torsion

Techniques for detecting torsion in Milnor fiber homology are outlined

Implications for further research in hyperplane arrangement topology

Abstract

As is well-known, the homology groups of the complement of a complex hyperplane arrangement are torsion-free. Nevertheless, as we showed in a recent paper [arXiv:1209.3414] the homology groups of the Milnor fiber of such an arrangement can have non-trivial integer torsion. We give here a brief account of the techniques that go into proving this result, outline some of its applications, and indicate some further questions that it brings to light.