The combinatorics of reducible Dehn surgeries
| dc.contributor.advisor | Gordon, Cameron, 1945- | en |
| dc.contributor.committeeMember | Gompf, Robert | en |
| dc.contributor.committeeMember | Luecke, John | en |
| dc.contributor.committeeMember | Reid, Alan | en |
| dc.contributor.committeeMember | Thompson, Abigail | en |
| dc.creator | Zufelt, Nicholas Troy | en |
| dc.date.accessioned | 2015-10-02T19:40:23Z | en |
| dc.date.accessioned | 2018-01-22T22:28:16Z | |
| dc.date.available | 2015-10-02T19:40:23Z | en |
| dc.date.available | 2018-01-22T22:28:16Z | |
| dc.date.issued | 2015-05 | en |
| dc.date.submitted | May 2015 | en |
| dc.date.updated | 2015-10-02T19:40:23Z | en |
| dc.description | text | en |
| dc.description.abstract | We study reducible Dehn surgeries on nontrivial knots in S³. The conjectured classification of such surgeries is known as the Cabling Conjecture, and partial progress toward the conjecture often comes in the form of a statement that an arbitrary reducible surgery resembles a cabled reducible surgery. One such resemblance is the Two Summands Conjecture: Dehn surgery on a knot in S³ can only produce a manifold with at most two irreducible connected summands. In the event that a reducible surgery on a knot K in S³ of slope r produces a manifold with more than two such summands, we show that |r| ≤ b, where b denotes the bridge number of K. As a consequence, we rule out this possibility for knots with b ≤ 5 and for positive braid closures. We also study reducible Dehn surgeries without the assumption that the reducible manifold contains more than two connected summands. Specifically, if P is an essential planar surface in the exterior of a hyperbolic knot which completes to a reducing sphere in this surgery, then it is shown that the number of boundary components of P is at least ten. | en |
| dc.description.department | Mathematics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier | doi:10.15781/T2QW29 | en |
| dc.identifier.uri | http://hdl.handle.net/2152/31514 | en |
| dc.subject | Dehn Surgery | en |
| dc.subject | Cabling conjecture | en |
| dc.subject | Knot theory | en |
| dc.subject | Low-dimensional topology | en |
| dc.title | The combinatorics of reducible Dehn surgeries | en |
| dc.type | Thesis | en |