Eulerian partitions for configurations of skew lines

Abstract

In this paper, which is a complement of [1], we study a few elementary invariants for configurations of skew lines, as introduced and analyzed first by Viro and his collaborators. We slightly simplify the exposition of some known invariants and use them to define a natural partition of the lines in a skew configuration.We also describe an algorithm which constructs a spindle-permutation for a given switching class, or proves non-existence of such a spindlepermutation.A spindle (or isotopy join or horizontal configuration) is a particularly nice configuration of skew lines in which all lines intersect an oriented additional line A, called the axis of the spindle. Its isotopy class