| Knot theory is all about understanding knotted circles in
3-dimensional space. Two knots are thought of as the same if one can be deformed to the other, without
cutting the circle or letting it pass through itself. The main motivating problem in the theory is to
find effective methods to decide whether or not two knots are really the same. We will explore this
problem, and the sorts of solutions that have been offered for it, especially in the context of the
"simplest" of all knots, the "unknot". |