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Double coverings of arrangement complements and $2$-torsion in Milnor fiber homology
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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.
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Topology of the icosidodecahedral arrangement
The icosidodecahedral arrangement, previously known to have torsion in the first integral homology of its Milnor fiber, is shown to be K(pi,1), and hence so is its Milnor fiber.
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