Cohomology rings and nilpotent quotients of real and complex arrangements

Details Cohomology rings and nilpotent quotients of real and complex arrangements Cohomology rings and nilpotent quotients of real and complex arrangements

1998-12-15

arxiv.org/abs/math/9812087v3

Arrangements--Tokyo 1998, 185-215, Advanced Studies in Pure Mathematics, vol. 27, Kinokuniya, Tokyo, 2000

Mathematics

Geometric Topology

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

Scientific paper

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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