Complements of hyperplane arrangements as posets of spaces

2015/02/12 by Michael W. Davis, Davis, Michael W.
Mathematics · #55N25 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1502.03650

openalex publication_date 2015/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The complement of an arrangement A of a finite number of affine hyperplanes in complex n-space has the structure of a poset of spaces indexed by the intersection poset, L(A). The space corresponding to G in L(A) is homotopy equivalent to the complement of the hyperplanes in the central arrangement A_G normal to G. This poset of spaces structure can be used to repair a spectral sequence argument in two earlier papers of Davis, Januszkiewicz, Leary and Okun for computing certain cohomology groups of arrangement complements. Similarly, toric hyperplane arrangements have the structure of a diagram of spaces and this structure can be used fix a spectral sequence argument in an earlier paper of Davis and Settepanella.

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