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Thesis Defense
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Jonathan Johnson, Virtual: Two-Bridge Links, Pretzel Knots, and Bi-Orderability
Wednesday, June 23, 2021, 02:00pm - 03:00pm
The left-orderability of a 3-manifold group is closely connected to the topological properties of the manifold. However, link groups are always left-orderable. Interestingly, there are link groups which are known to be bi-orderable, as well as link groups known not to be bi-orderable. In this talk, I will discuss a couple of results on the bi-orderability of link groups and how these results are related to properties of the cyclic branched covers of a knot. If a two-bridge link has Alexander polynomial with coprime coefficients and all real positive roots, then its link group is bi-orderable. This result shows that a large family of knots whose cyclic branched covers are known to be L-spaces have bi-orderable knot groups. Additionally, many genus one pretzel knots have bi-orderable knot groups including the $P(-3, 3, 2r+1)$ pretzel knots. Issa-Turner showed that all the cyclic branched covers of these knots are L-spaces. There is also a family of genus one pretzel knots with bi-orderable knot groups and double branched covers which are not L-spaces. This talk is a thesis defense. ID: 952 3915 2304 Code: Bi-order
Location: Virtual

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