The monodromy group of a configuration of lines

A configuration of skew lines is an unordered collection of lines in general position in a real affine or projective three-dimensional space. Such configurations give rise to topological problems related to real algebraic geometry. In this paper, the notion of a monodromy group, which is a rigid isotopy invariant of such configurations, is introduced, and some of its properties are studied. It is shown that in two important cases, the monodromy group determines the configuration up to rigid isotopy and mirror image.