I mostly like to think about knots in 3-manifolds. Currently, I'm trying to understand when the fundamental group of the complement of a knot in S3 is bi-orderable, i.e. has a total order invariant under both left and right multiplication. Some examples of knots with bi-orderable knot groups are the figure 8 knot, the stevedore knot, and the pretzel knot P(-3,3,3). Typically, knot groups are not bi-orderable so naturally one wonders, "When a knot does have a bi-orderable knot group what does this tell us about the topology of the knot?" This is the motivating question behind my research.
Publications and Work in Progress
♦ Residual Torsion-Free Nilpotence, Bi-Orderability and Pretzel Knots (preprint)
♦ Two-Bridge Knots and Residual Torsion-Free Nilpotence (preprint)