Title:
Legendrian large cables and non-uniformly thick knots
Legendrian large cables and non-uniformly thick knots
| dc.contributor.advisor | Etnyre, John B. | |
| dc.contributor.advisor | Ghomi, Mohammad | |
| dc.contributor.author | McCullough, Andrew | |
| dc.contributor.committeeMember | Hom, Jennifer | |
| dc.contributor.committeeMember | Margalit, Dan | |
| dc.contributor.committeeMember | Matic, Gordana | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2020-09-08T12:38:19Z | |
| dc.date.available | 2020-09-08T12:38:19Z | |
| dc.date.created | 2019-08 | |
| dc.date.submitted | August 2019 | |
| dc.date.updated | 2020-09-08T12:38:19Z | |
| dc.description.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. | |
| dc.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/63488 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | Low dimensional topology | |
| dc.subject | Legendrian knots | |
| dc.subject | Contact structures | |
| dc.title | Legendrian large cables and non-uniformly thick knots | |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Ghomi, Mohammad | |
| local.contributor.advisor | Etnyre, John B. | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isAdvisorOfPublication | 2ff77925-db3c-48d6-abc8-b3dfbc983cd1 | |
| relation.isAdvisorOfPublication | a9264768-2f0a-4f64-842d-cff98031262b | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 | |
| thesis.degree.level | Doctoral |