Knot Theory

Knot theory is a branch of topology concerned with the classification of knots. A knot is represented by a string with its ends tied together and two such strings represent the same knot if they can be transformed into each other without cutting. Knot theorists invent and study invariants of knots. These are simply functions that to each knot assign a number or a polynomial or .... The ideal knot invariant should be easily computable and should take different values on different knots. Such an invariant has not yet been found and the search is still on! However, substantial progress was made, particularly over the last 15 years. Check out knotscape -- a computer program that computes various knot invariants (and much more). Pictures of knots, such as the one on the right, can be drawn by knotplot.

For the theoretical background on knots and their invariants, look at the book

Colin C. Adams: "The Knot Book", W.H. Freeman and Company, Oxford 1994.

This book is great fun to read and there is a copy in the Undergraduate Collection.