Colloquium
3:30 p.m., Monday, January 8
Math 100
Bert Wiest
PIMS and Department of Mathematics, UBC
Orderable groups in topology
In the last few years it has been realized that many of the
groups that appear most naturally in lowdimensional topolgy are
orderable. This means, their elements can be totally ordered in a way
which is compatible with the group structure: g < h implies kg < kh
for g,h,k in the group. Orderability is a stronger condition that
torsionfreeness. First I want to explain the concept, and geometric
significance of orderability. Then I want to talk about two classes of
examples that I'm particularly interested in: (1) braid groups and their
generalisations, and (2) fundamental groups of 3manifolds. In both
cases, I want to show how the problem of ordering these groups has
shed new light on existing theory, and has sometimes revealed fascinating
new problems.
