Hyperplane arrangements and Milnor fibrations

TL;DR

This paper explores the topological relationships among spaces associated with complex hyperplane arrangements, using cohomology with local systems to analyze their homology and monodromy operators.

Contribution

It introduces a cohomological approach with local systems to study the homology and monodromy of related topological spaces in hyperplane arrangements.

Findings

Cohomology with local systems reveals homological properties of arrangement spaces.

Monodromy operators are characterized through this cohomological framework.

Interrelations among the complement, boundary manifold, and Milnor fiber are clarified.

Abstract

There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.