UBC

Wed 22 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133

Generalized torsion in knot groups

ESB 4133
Wed 22 Oct 2014, 3:15pm4:15pm
Abstract
Classical knot groups, that is fundamental groups of knot complements in 3space, are known to be torsionfree. However, we show that for many knots, their groups contain generalized torsion: a nontrivial element such that some product of conjugates of that element equals the identity. One example (the hyperbilic knot 5_2) was discovered with the aid of a Python program written by the USRA student Geoff Naylor. Other examples include torus knots, algebraic knots in the sense of Milnor (arising from singularities of complex curves) and satellites of knots whose groups contain generalized torsion. Although all knot groups are leftorderable, the existence of generalized torsion is an obstruction to their being biorderable.
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University of Utah

Wed 29 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133


ESB 4133
Wed 29 Oct 2014, 3:15pm4:15pm
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