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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Topology of factored arrangements of lines
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by Luis Paris
Proc. Amer. Math. Soc. 123 (1995), 257-261
DOI: https://doi.org/10.1090/S0002-9939-1995-1227528-7

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.
References
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • 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