MA0322 KNOTS

David E. Evans

Knots are closed strings in three dimensional space. The fundamental question is to decide when two given knots are the same or if a particular knot is equivalent to another or even knotted at all. Knots have been studied by mathematicians for over a century but in the last 15 years a number of new simple ideas have contributed to remarkable breakthroughs which have helped clear up a large number of outstanding problems and conjectures. These ideas have come from a number of branches of mathematics and not only have influenced knot theory itself but have revolutionised several branches of mathematics and even mathematical physics. Applications have also been found in biology in understanding how DNA strands are knotted. This course is an elementary introduction to modern knot theory as it now stands and some of the tools which are now available for understanding knots.

DIAGRAMS AND NOTES
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Useful texts:

L Kauffman: Knots and Physics, World Scientific Press
ND Gilbert and T Porter: Knots and Surfaces, Oxford University Press
CC Adams: The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, W.H. Freeman & Company
P Cromwell: Knots and Links
WBR Lickorish: An Introduction to Knot Theory, Springer
DE Evans and Y Kawahigashi: Quantum Symmetries on Operator Algebras, Oxford University Press, 1998