Legendrian Large Cables

Dissertation Defense
Tuesday, April 9, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Andrew McCullough – Georgia Institute of Technology – andrew.mccullough@gatech.eduhttp://people.math.gatech.edu/~crustin3/
Andrew McCullough

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.