Title:
Legendrian large cables and non-uniformly thick knots
Legendrian large cables and non-uniformly thick knots
Author(s)
McCullough, Andrew
Advisor(s)
Etnyre, John B.
Ghomi, Mohammad
Ghomi, Mohammad
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Abstract
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.
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Dissertation