**Monday 30 January 2023**

**15:00–16:30***

**Anca Măcinic (IMAR)** — *On the decomposable Orlik-Solomon algebra*

We prove that the decomposable Orlik-Solomon algebra associated to a simple matroid on ground set [n] is torsion free, in all degrees.

This holds in particular for the decomposable OS algebra associated to an arrangement of hyperplanes. In the class of hypersolvable & non-supersolvable complex hyperplane arrangements, the torsion freeness, in a certain degree, of this combinatorially defined object (i.e. determined by 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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