If we take two knots (or links) at random, what we would like to have is an efficient method that will determine for us whether or not they are equivalent knots (or links). In general, sadly, such an efficient method has yet to be discovered. So, at present a concise classification of knots is not possible. The next most obvious step is to try to group together knots (or links) with a particular property or properties in common, and then try to classify them. In fact, the techniques we have already discussed are sufficient for us to extract the characteristics of certain particular types of knots.
KeywordsSolid Torus Reidemeister Move Alexander Polynomial Seifert Surface Borromean Ring
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