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Spindle configurations of skew lines

Roland Bacher·David Garber
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Abstract

We prove a conjecture of Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. We use this result in order to define an invariant, spindle-genus, for spindle-configurations. We also slightly simplify the exposition of some known invariants for configurations of skew lines and use them to define a natural partition of the lines in a skew configuration. Finally, we describe an algorithm which constructs a spindle in a given switching class, or proves non-existence of such a spindle.

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Roland Bacher, David Garber. 2005-06-16. Spindle configurations of skew lines. https://doi.org/10.2140/gt.2007.11.1049

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