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Generalized torsion in knot groups
by
Dale Rolfsen
University of British Columbia
Coauthors: Geoff Naylor
In a group, a nonidentity element is called a generalized torsion element if some product of its conjugates equals the identity. We show that for many classical knots one can find generalized torsion in the fundamental group of its complement, commonly called the knot group. It follows that such a group is not bi-orderable. Examples include all torus knots, the (hyperbolic) knot 52 and algebraic knots in the sense of Milnor. We also identify many knots whose groups do not have generalized torsion elements.
Date received: November 30, 2014
Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-12.