Pretzel knots of length three with unknotting number one
| dc.contributor.advisor | Gordon, Cameron, 1945- | en |
| dc.contributor.committeeMember | Gompf, Robert | en |
| dc.contributor.committeeMember | Luecke, John | en |
| dc.contributor.committeeMember | Namazi, Hossein | en |
| dc.contributor.committeeMember | Ozsvath, Peter | en |
| dc.contributor.committeeMember | Reid, Alan | en |
| dc.creator | Staron, Eric Joseph | en |
| dc.date.accessioned | 2012-07-12T20:49:44Z | en |
| dc.date.accessioned | 2017-05-11T22:25:50Z | |
| dc.date.available | 2012-07-12T20:49:44Z | en |
| dc.date.available | 2017-05-11T22:25:50Z | |
| dc.date.issued | 2012-05 | en |
| dc.date.submitted | May 2012 | en |
| dc.date.updated | 2012-07-12T20:49:50Z | en |
| dc.description | text | en |
| dc.description.abstract | This thesis provides a partial classification of all 3-stranded pretzel knots K=P(p,q,r) with unknotting number one. Scharlemann-Thompson, and independently Kobayashi, have completely classified those knots with unknotting number one when p, q, and r are all odd. In the case where p=2m, we use the signature obstruction to greatly limit the number of 3-stranded pretzel knots which may have unknotting number one. In Chapter 3 we use Greene's strengthening of Donaldson's Diagonalization theorem to determine precisely which pretzel knots of the form P(2m,k,-k-2) have unknotting number one, where m is an integer, m>0, and k>0, k odd. In Chapter 4 we use Donaldson's Diagonalization theorem as well as an unknotting obstruction due to Ozsv\'ath and Szab\'o to partially classify which pretzel knots P(2,k,-k) have unknotting number one, where k>0, odd. The Ozsv\'ath-Szab\'o obstruction is a consequence of Heegaard Floer homology. Finally in Chapter 5 we explain why the techniques used in this paper cannot be used on the remaining cases. | en |
| dc.description.department | Mathematics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.slug | 2152/ETD-UT-2012-05-5055 | en |
| dc.identifier.uri | http://hdl.handle.net/2152/ETD-UT-2012-05-5055 | en |
| dc.language.iso | eng | en |
| dc.subject | Topology | en |
| dc.subject | Knot theory | en |
| dc.subject | Unknotting number | en |
| dc.subject | Heegaard Floer homology | en |
| dc.title | Pretzel knots of length three with unknotting number one | en |
| dc.type.genre | thesis | en |