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 low-dimensional 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 torsion-freeness. 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 3-manifolds. 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.

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