Anca Daniela Macinic | Searcharxiv

arXiv2008

Cohomology rings and formality properties of nilpotent groups

We introduce partial formality and relate resonance with partial formality properties. For instance, we show that for finitely generated nilpotent groups that are k-formal, the resonance varieties are trivial up to degree k. We also show that the cohomology ring of a nilpotent k-formal group is generated in degree 1, up to degree k+1; this criterion is necessary and sufficient for 2-step nilpotent groups to be k-formal. We compute resonance varieties for Heisenberg-type groups and deduce the degree of partial formality for this class of groups.

math.AT↗

arXiv2007

On the monodromy action on Milnor fibers of graphic arrangements

We analyze the monodromy action, over the rationals, on the first homology group of the Milnor fiber, for arbitrary subarrangements of Coxeter arrangements. We propose a combinatorial formula for the monodromy action, involving Aomoto complexes in positive characteristic. We verify the formula, in cases A, B and D.

math.AG↗