Cohomology rings and nilpotent quotients of real and complex arrangements

Daniel Matei; Alexander I. Suciu

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arXiv · math/9812087

Cohomology rings and nilpotent quotients of real and complex arrangements

Daniel Matei·Alexander I. Suciu

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Abstract

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.

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BibTeX RIS

Daniel Matei, Alexander I. Suciu. 1999-04-03. Cohomology rings and nilpotent quotients of real and complex arrangements. https://arxiv.org/abs/math/9812087

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