Cohomology rings and formality properties of nilpotent groups

Details Cohomology rings and formality properties of nilpotent groups Cohomology rings and formality properties of nilpotent groups

2008-01-31

arxiv.org/abs/0801.4847v1

Journal of Pure and Applied Algebra 214 (2010), pp. 1818-1826

Mathematics

Algebraic Topology

18 pages

Scientific paper

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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