Spindle configurations of skew lines

Details Spindle configurations of skew lines Spindle configurations of skew lines

2002-05-23

arxiv.org/abs/math/0205245v3

Mathematics

Geometric Topology

42 pages, many figures. A new corrected proof of a conjecture of Crapo and Penne is added. More new material is also added

Scientific paper

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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