Key words and phrases: Projective configurations, skew lines, isotopies and rigid isotopies, mirror configurations, join

1991 Mathematics Subject Classification: Primary 51H10, 51A20; Secondary 05B30, 51E30

Abstract:

This is a survey of results on projective configurations of subspaces in general position. It is written in the form of popular introduction to subject, with much of the material accessible to advanced high school students. However, in the second half of the text we make an honest attempt give a complete survey about configurations of lines in general position in three-dimensional space.

• Introduction
• Two Lines
• Orientations and Semi-Orientations
• The Linking Number
• Triples of Lines
• Amphicheiral and Nonamphicheiral Sets
• Four Lines
• Isotopic Lines of an Interlacing
• Five Lines
• Six Lines
• Seven Lines
• Interlacings of Labeled Lines
• Not Only Lines Can be Interlaced
• Plane Configurations of Lines
• High-Dimensional Generalizations of Interlacings of Lines
• Connection with Real Algebraic Surfaces of Degree $4$
• Bibliography
• About this document ...