Generalized torsion in knot groups

Dale Rolfsen (University of British Columbia)

Monday 20th April, 2015 16:00-17:00 Maths 204


A generalized torsion element of a group is a nonidentity element for which some product of its conjugates equals the identity.  The existence of such elements is an obstruction to a group being orderable, that is having a strict total ordering of its elements which is invariant under multiplication on both sides.  We show that many classical knots have generalized torsion in their groups, that is the fundamental group of the complement in 3-space.  Examples are torus knots, algebraic knots in the sense of Milnor, cabled knots and also some hyperbolic knots.  There are also many knots whose groups do not have generalized torsion; indeed the groups are bi-orderable.

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