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arXiv · 0801.4847

Cohomology rings and formality properties of nilpotent groups

Anca Daniela Macinic
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Abstract

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.

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Anca Daniela Macinic. 2008-01-31. Cohomology rings and formality properties of nilpotent groups. https://arxiv.org/abs/0801.4847

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