3:30 p.m., Friday
Professor Dale Rolfsen
Department of Mathematics
Ordered groups and braids
The braid groups B_n continue to surprise us, although they
were introduced by Emil Artin 75 years ago. They have played a big
role in topology, analysis, group theory and mathematical physics.
For example, Vaughan Jones' discovery of new representations of B_n
fifteen years ago led to a revolution in the theory of knots. One of
the most astonishing recent discoveries is that the braid
groups are actually right-orderable: there is a strict total ordering
of all braids which is preserved under multiplication on the right.
This was proved by Dehornoy, using techniques motivated by set theory
and large cardinals. Since then, others (including myself) have found
a natural geometric way of understanding this ordering, using
techniques which are very different from the usual arguments in
ordered group theory. I will discuss this ordering and some of its
consequences, and a website which can decide the ordering.
Refreshments will be served in Math Annex Room 1115, 3:15 p.m.