Behavior of knot Floer homology under conway and genus two mutation
| dc.contributor.advisor | Gordon, Cameron, 1945- | |
| dc.creator | Moore, Allison Heather | en |
| dc.date.accessioned | 2013-10-23T17:35:48Z | en |
| dc.date.accessioned | 2017-05-11T22:35:03Z | |
| dc.date.available | 2017-05-11T22:35:03Z | |
| dc.date.issued | 2013-05 | en |
| dc.date.submitted | May 2013 | en |
| dc.date.updated | 2013-10-23T17:35:48Z | en |
| dc.description | text | en |
| dc.description.abstract | In this dissertation we prove that if an n-stranded pretzel knot K has an essential Conway sphere, then there exists an Alexander grading s such that the rank of knot Floer homology in this grading, [mathematical equation], is at least two. As a consequence, we are able to easily classify pretzel knots admitting L-space surgeries. We conjecture that this phenomenon occurs more generally for any knot in S³ with an essential Conway sphere. We also exhibit an infinite family of knots, each of which admits a nontrivial genus two mutant which shares the same total dimension of knot Floer homology, while being distinguished by knot Floer homology as a bigraded invariant. Additionally, the genus two mutation interchanges the [mathematical symbol]-graded knot Floer homology groups in [mathematical symbol]-gradings k and -k. This infinite family of examples supports a second conjecture, namely that the total rank of knot Floer homology is invariant under genus two mutation. | en |
| dc.description.department | Mathematics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/2152/21684 | en |
| dc.language.iso | en_US | en |
| dc.subject | Knot theory | en |
| dc.subject | Heegaard Floer homology | en |
| dc.subject | Pretzel knots | en |
| dc.subject | Mutation | en |
| dc.title | Behavior of knot Floer homology under conway and genus two mutation | en |