Dale Rolfsen
(University of British Columbia)
Friday 28th January, 12.05-12.55pm, 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 (left-orderable), the pure braid groups
(bi-orderable) and the fundamental groups of almost all surfaces and many
3-dimensional manifolds. In particular, all classical knot groups are
left-orderable and some are bi-orderable. For example the figure-eight
knot group is bi-orderable, while the trefoil's group is only
left-orderable. I will discuss this, as well as some of the algebraic
consequences of the existence of invariant orderings.
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