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NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT
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Geometry-Algebra-Singularities-Combinatorics Seminar
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Cohomology rings, nilpotent quotients, and resonance varieties
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(Northeastern University)
Northeastern University 509 Lake Hall 1:30 p.m., Monday, April 12, 1999
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Abstract: The cohomology ring of a space X is intricately connected to the nilpotent quotients of its fundamental group G. I will talk about one such connection, and certain invariants that arise out of this connection. The main result is an explicit correspondence between two sets of invariants - one determined by the vanishing cup products in the degree 2 truncation of the cohomology ring of X, the other by the prime-index subgroups of the second nilpotent quotient G/G3. The "resonance varieties" that appear in this correspondence may be interpreted as the determinantal varieties of the linearized Alexander matrix of G.
I will illustrate with certain classes of spaces - including complements of complex hyperplane arrangements, and complements of arrangements of transverse planes in R4 - for which the invariants are amenable to combinatorial interpretations, capable of yielding classification results.
This is joint work with Daniel Matei. A paper describing these results may be found at math.GT/9812087.
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Geometry-Algebra-Singularities-Combinatorics home page:
http://www.math.neu.edu/~suciu/GASC.html
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