Classical Knot Invariants
A knot (or link) invariant, by its very definition, as discussed in the previous chapter, does not change its value if we apply one of the elementary knot moves. As we have already seen, it is often useful to project the knot onto the plane, and then study the knot via its regular diagram. If we wish to pursue this line of thought, we must now ask ourselves what happens to, what is the effect on, the regular diagram if we perform a single elementary knot move on it? This question was studied by K. Reidemeister in the 1920s. In the course of time, many knot invariants were defined from Reidemeister’s seminal work. In this chapter, in addition to discussing these types of knot invariants, we shall also look at knot invariants that follow naturally from what one might say is mathematical experience.
KeywordsInternal Part Reidemeister Move Polygonal Curve Jordan Curve Theorem Oriented Link
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