The Theory of Links
## An Introduction to the Theory of Links

During the past few years, we have presented an outline of the **Theory of Knots**, and
in particular we have discussed the problem of **Knot Tabulation**. Readers interested
in this discussion are referred to
**the relevant pages**.

It turns out, however, that knots are merely a specific case of a more extended class of
mathematical objects, which are usually referred to as **links**. While knots are
formally defined as ambient isotopy classes of continuous one-to-one functions from the
circle to the three-dimensional sphere, links are ambient isotopy classes of continuous
one-to-one functions from a *union of any number of circles* to the three-dimensional
sphere. This means that knots are a special example of links, where this "any number of
circles" is equal to one.

In plain language: a knot may be indicated by drawing a closed line that does not intersect
itself, while a link may be indicated by drawing a collection of closed lines, each of whom
does not intersect itself, and no two such lines intersect each other.

Starting from the current page, we are going to extend the discussion from knots to
links. We shall start by pointing out which aspects of the theory of knots are also
applicable to links, and which aspects will now have to be modified. We are then going to
continue with the problem of *Tabulation of Links*, where a number of new challenges
emerges. Finally we are going to provide the reader with specific results.

To continue this discussion, please click **here**.

Charilaos Aneziris

**Copyright 2001**

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