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

Masahiko Yoshinaga

doi:10.1007/s40879-019-00387-8

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arXiv · 1902.06256

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

Masahiko Yoshinaga

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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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BibTeX RIS

Masahiko Yoshinaga. 2019-02-17. Double coverings of arrangement complements and $2$-torsion in Milnor fiber homology. https://doi.org/10.1007/s40879-019-00387-8

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