Double coverings of arrangement complements and $2$-torsion in Milnor fiber homology

Abstract

We prove that the mod $2$ Betti numbers of double coverings of a complex hyperplane arrangement complement are combinatorially determined. The proof is based on a relation between the mod $2$ Aomoto complex and the transfer long exact sequence. Applying the above result to the icosidodecahedral arrangement ($16$ planes in the three dimensional space related to the icosidodecahedron), we conclude that the first homology of the Milnor fiber has non-trivial $2$-torsion.

14 pages, 5 figures, to appear in European Journal of Mathematics

References in corpus (2)

• On the monodromy action on Milnor fibers of graphic arrangements
• Homology graph of real arrangements and monodromy of Milnor Fiber

Cited by in corpus (3)

• Milnor fibrations of arrangements with trivial algebraic monodromy
• Cohomology, Bocksteins, and resonance varieties in characteristic 2
• The homology groups of finite cyclic covering of line arrangement complement