A Long Exact Sequence in Cohomology for Deleted and Restricted Subspaces Arrangements
نویسنده
چکیده
The notions of deleted and restricted arrangements have been very useful in the study of arrangements of hyperplanes. Let A be an arrangement of hyperplanes and x ∈ A. The deleted and restricted arrangements A and A allows us to compute recursively the Poincaré polynomials of the complement space M(A) with the following formula : Poin(M(A), t) = Poin(M(A′), t) + tPoin(M(A′′), t). In this paper, we consider the extension of this formula to arbitrary subspaces arrangements. The main result is the existence of a long exact sequence connecting the rational cohomology of M(A), M(A) and M(A). Using this sequence, we obtain new results connecting the Betti numbers and Poincaré polynomials of deleted and restricted arrangements.
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تاریخ انتشار 2008