Abstract
LetV be a finite dimensional vector space over the real or complex numbers. Areal (orcomplex)arrangement A inV is a finite collection of real (or complex) affine hyperplanes. A real arrangement inV can becomplexified to form a complex arrangement in the complex vector spaceA. The (complex)complement of a real arrangementA is defined byM(A)=V⊗ℂ−⋃ H∈ A H⊗ℂ. There are two different finite simplicial complexes which carry the homotopy type ofM(A), one given by M. Salvetti, the other by P. Orlik. In this paper we describe both complexes and exhibit a simplicial homotopy equivalence between them.
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References
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P. Orlik, Complements of Subspace Arrangements, to appear
M. Salvetti, Topology of the complement of real hyperplanes in ℂN,Invent. math. 88 (1987), 603–618
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Arvola, W.A. Complexified real arrangements of hyperplanes. Manuscripta Math 71, 295–306 (1991). https://doi.org/10.1007/BF02568407
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DOI: https://doi.org/10.1007/BF02568407