The University of Sydney
School of Mathematics and Statistics  
Algebra Seminar  
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University of Sydney Algebra Seminar

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.