Monday 30 January 2023
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.
* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.