Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 45, No. 1, pp. 133-153 (2004)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 1, pp. 133-153 (2004) |
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Unbounded regions in an arrangement of lines in the planeAlan WestSchool of Mathematics, University of Leeds, Leeds LS2 9JT, EnglandAbstract: We take a set $\Omega$ of $n$ points and an arrangement $\Sigma$ of $m$ lines in the plane which avoid these points but separate any two of them. We suppose these satisfy the following unboundedness property: for each point $x \in \Omega$ there is a homotopy from $\Sigma$ to ${\Sigma}'$ avoiding $\Omega$ so that $x$ is in an unbounded component of the complement of ${\Sigma}'$. It is proved that then $n \leq 2m$. This result is required to partially solve a problem in differential geometry which is described briefly. Full text of the article:
Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
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