Degree Date
2022
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Abstract
We use the functoriality of Khovanov homology to examine the smooth, boundary-preserving isotopy of surfaces embedded in the 4-ball. We exemplify an infinite family of prime knots that bound an arbitrarily-large number of smoothly-distinct slice disks by distinguishing the maps they induce on Khovanov homology. Similar techniques produce an infinite family of knots that each bound a pair of exotic surfaces of arbitrary genus.
Citation
Sundberg, I. 2022. "Khovanov Homology & Uniqueness of Surfaces in the 4-ball." PhD Diss., Bryn Mawr College.