Hyperplane arrangements and Milnor fibrations

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.

52 pages, 7 figures; accepted for publication in the Annales de la Faculté des Sciences de Toulouse

References in corpus (6)

• Algebraic invariants for right-angled Artin groups
• On the monodromy action on Milnor fibers of graphic arrangements
• Boundary manifolds of projective hypersurfaces
• Characteristic varieties and Betti numbers of free abelian covers
• The boundary manifold of a complex line arrangement
• Geometric and homological finiteness in free abelian covers

Cited by in corpus (10)

• The Milnor fibration of a hyperplane arrangement: from modular resonance to algebraic monodromy
• Around the tangent cone theorem
• Abelian duality and propagation of resonance
• Double coverings of arrangement complements and $2$-torsion in Milnor fiber homology
• On the monodromy of Milnor fibers of hyperplane arrangements
• Poincaré duality and resonance varieties
• Milnor fibrations of arrangements with trivial algebraic monodromy
• Cohomology, Bocksteins, and resonance varieties in characteristic 2
• Dynamical systems on some elliptic modular surfaces via operators on line arrangements
• The homology groups of finite cyclic covering of line arrangement complement