18.095 Lecture Notes - Lecture 7: Linking Number
Document Summary
How to detect if a given closed loop in three dimensional space is knotted and how to understand if one closed loop is deformable to another. Things we can compute from a particular instance of a knot, but that does change under deformations. Methods for encoding knots (and links) as well as rules for understanding when two different codings are given equivalent knots. Things we can computer from a particular encoding of the knot but that do not agree for different encodings of the same knot. Projections can be alternating: as you move along the knot over and under crossings alternate. Gauss code or gauss diagram: label the crossings (say by 1, 2, , n) Pick a base point on the knot and an orientation. Run along the knot and write down the label of the crossing you meet with an o if you are going over and u if you are going under.
