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arXiv · 2212.12275

On torsion freeness for the decomposable Orlik-Solomon algebra

Anca Macinic
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Abstract

We prove the torsion freeness of the decomposable Orlik--Solomon algebra of a simple matroid on ground set $[n]$. In the class of hypersolvable \& non-supersolvable complex hyperplane arrangements, the torsion freeness, in a certain degree, of this combinatorially defined object, associated to the intersection lattice of the arrangement, impacts on the first non-vanishing higher homotopy group of the complement of the arrangement.

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Anca Macinic. 2023-02-21. On torsion freeness for the decomposable Orlik-Solomon algebra. https://arxiv.org/abs/2212.12275

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