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arXiv · 1503.05721

The $\textbf{nbc}$ minimal complex of supersolvable arrangements

Simona Settepanella·Michele Torielli
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Abstract

In this paper we give a very natural description of the bijections between the minimal CW-complex homotopy equivalent to the complement of a supersolvable arrangement $\mathcal{A}$, the $\textbf{nbc}$ basis of the Orlik-Solomon algebra associated to $\mathcal{A}$ and the set of chambers of $\mathcal{A}$. We use these bijections to get results on the first (co)homology group of the Milnor fiber of $\mathcal{A}$ and to describe a bijection between the symmetric group and the $\textbf{nbc}$ basis of the braid arrangement.

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Simona Settepanella, Michele Torielli. 2015-03-19. The $\textbf{nbc}$ minimal complex of supersolvable arrangements. https://arxiv.org/abs/1503.05721

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