A long exact sequence in cohomology for deleted and restricted subspaces arrangements

2007/09/04 by Gery Debongnie, Debongnie, Gery
Mathematics · #55P62 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55P62

paper · pdf · doi:10.48550/arxiv.0709.0373

11 pages

arxiv created 2007/09/04 · arxiv updated 2009/12/01

Abstract

The notions of deleted and restricted arrangements have been useful in the study of arrangements of hyperplanes. If A is an arrangement of hyperplanes, x in A and A', A'' the deleted and restricted arrangements, there is a formula connecting the Poincare polynomials of the complement spaces M(A), M(A') and M(A''). 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 Poincare polynomials of deleted and restricted arrangements.

Related

• Length and decomposition of the cohomology of the complement to a\n hyperplane arrangement
• Deletion-restriction in toric arrangements
• Complements of hyperplane arrangements as posets of spaces
• Hyperplane arrangements, M-tame polynomials and twisted cohomology
• Addition-deletion theorems for the Solomon-Terao polynomials and B-sequences of hyperplane arrangements