Dale Rolfsen
(University of British Columbia)
Friday 28th January, 12.0512.55pm, Carslaw 157
Ordering braid groups and knot groups
It has recently been realized that many groups of interest to
topologists can be given a strict total ordering which is invariant under
left multiplication, or even by multiplication on both sides. Examples
are the Artin braid groups (leftorderable), the pure braid groups
(biorderable) and the fundamental groups of almost all surfaces and many
3dimensional manifolds. In particular, all classical knot groups are
leftorderable and some are biorderable. For example the figureeight
knot group is biorderable, while the trefoil's group is only
leftorderable. I will discuss this, as well as some of the algebraic
consequences of the existence of invariant orderings.
