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Cohomology rings and nilpotent quotients of real and complex arrangements

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în volumul unei conferinţe

Autori: D. Matei, A.I. Suciu

Editorial: Arrangements--Tokyo 1998, M. Falk, H. Terao, Advanced Studies in Pure Mathematics, 27, p.185-215, 2000.


For an arrangement with complement X and fundamental group G, we relate the truncated cohomology ring, H^{<=2}(X), to the second nilpotent quotient, G/G_3. We define invariants of G/G_3 by counting normal subgroups of a fixed prime index p, according to their abelianization. We show how to compute this distribution from the resonance varieties of the Orlik-Solomon algebra mod p. As an application, we establish the cohomology classification of 2-arrangements of n<=6 planes in R^4.

Cuvinte cheie: cohomology ring, nilpotent quotient, real and complex arrangements, resonance varieties