Friday, March 12, 1999, 14:00 / HSS 2.01.12

E. Christopher Zeeman, F.R.S., K.B.

Introduction to Knot Theory

A knot is a closed curve in three dimensions that cannot be moved into a circle. We shall prove that knots exist. We introduce an invariant that distinguishes between different knots. Knots are similar to the integers in that they have a commutative associative product, and unique factorization into primes. Here is a list of all the primes with less than eight crossings. In 4 dimensions any curve can be unknotted, but a sphere can be tied in a knot. In 5 dimensions any sphere can be unknotted, but two spheres can be linked. Guess the dimensions in which 100-dimensional spheres can be knotted and linked. An informal reception follows the talk. Students are encouraged to attend! Download the poster.

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