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Georgia Tech

1. McCullough, Andrew. Legendrian large cables and non-uniformly thick knots.

Degree: PhD, Mathematics, 2020, Georgia Tech

We define the notion of a knot type having Legendrian large cables and show that having this property implies that the knot type is not uniformly thick. Moreover, there are solid tori in this knot type that do not thicken to a solid torus with integer sloped boundary torus, and that exhibit new phenomena; specifically, they have virtually overtwisted contact structures. We then show that there exists an infinite family of ribbon knots that have Legendrian large cables. These knots fail to be uniformly thick in several ways not previously seen. We also give a general construction of ribbon knots, and show when they give similar such examples. Advisors/Committee Members: Etnyre, John B (advisor), Ghomi, Mohammad (advisor), Hom, Jennifer (committee member), Margalit, Dan (committee member), Matic, Gordana (committee member).

Subjects/Keywords: Low Dimensional Topology. Legendrian Knots. Contact Structures.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

McCullough, A. (2020). Legendrian large cables and non-uniformly thick knots. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/63488

Chicago Manual of Style (16th Edition):

McCullough, Andrew. “Legendrian large cables and non-uniformly thick knots.” 2020. Doctoral Dissertation, Georgia Tech. Accessed September 20, 2020. http://hdl.handle.net/1853/63488.

MLA Handbook (7th Edition):

McCullough, Andrew. “Legendrian large cables and non-uniformly thick knots.” 2020. Web. 20 Sep 2020.

Vancouver:

McCullough A. Legendrian large cables and non-uniformly thick knots. [Internet] [Doctoral dissertation]. Georgia Tech; 2020. [cited 2020 Sep 20]. Available from: http://hdl.handle.net/1853/63488.

Council of Science Editors:

McCullough A. Legendrian large cables and non-uniformly thick knots. [Doctoral Dissertation]. Georgia Tech; 2020. Available from: http://hdl.handle.net/1853/63488

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