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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Topology of factored arrangements of lines


Author: Luis Paris
Journal: Proc. Amer. Math. Soc. 123 (1995), 257-261
MSC: Primary 52B30; Secondary 55P20
DOI: https://doi.org/10.1090/S0002-9939-1995-1227528-7
MathSciNet review: 1227528
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Abstract: A real arrangement of affine lines is a finite family $ \mathcal{A}$ of lines in $ {{\mathbf{R}}^2}$. A real arrangement $ \mathcal{A}$ of lines is said to be factored if there exists a partition $ \Pi = ({\Pi _1},{\Pi _2})$ of $ \mathcal{A}$ into two disjoint subsets such that the Orlik-Solomon algebra of $ \mathcal{A}$ factors according to this partition. We prove that the complement of the complexification of a factored real arrangement of lines is a $ K(\pi ,1)$ space.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1227528-7
Article copyright: © Copyright 1995 American Mathematical Society

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