Cohomology rings and nilpotent quotients of real and complex arrangements

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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.
LaTeX2e, 22 pages, to appear in Singularities and Arrangements, Sapporo-Tokyo 1998, Advanced Studies in Pure Mathematics

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Geometric Topology, Algebraic Geometry, 52B30, 57M05 (Primary); 20F14, 20J05 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/77848

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9812087
 http://arxiv.org/abs/math/9812087
 Arrangements--Tokyo 1998, 185-215, Advanced Studies in Pure Mathematics, vol. 27, Kinokuniya, Tokyo, 2000

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arXiv