Spindle configurations of skew lines
Geometric Topology
2014-11-11 v3 Combinatorics
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.
Cite
@article{arxiv.math/0205245,
title = {Spindle configurations of skew lines},
author = {Roland Bacher and David Garber},
journal= {arXiv preprint arXiv:math/0205245},
year = {2014}
}
Comments
42 pages, many figures. A new corrected proof of a conjecture of Crapo and Penne is added. More new material is also added