Boring split links
| dc.creator | Taylor, Scott A. | |
| dc.date | 2007-09-26 | |
| dc.date | 2009-01-15 | |
| dc.date.accessioned | 2026-07-07T12:29:20Z | |
| dc.date.available | 2026-07-07T12:29:20Z | |
| dc.description | Boring is an operation which converts a knot or two-component link in a 3--manifold into another knot or two-component link. It generalizes rational tangle replacement and can be described as a type of 2--handle attachment. Sutured manifold theory is used to study the existence of essential spheres and planar surfaces in the exteriors of knots and links obtained by boring a split link. It is shown, for example, that if the boring operation is complicated enough, a split link or unknot cannot be obtained by boring a split link. Particular attention is paid to rational tangle replacement. If a knot is obtained by rational tangle replacement on a split link, and a few minor conditions are satisfied, the number of boundary components of a meridional planar surface is bounded below by a number depending on the distance of the rational tangle replacement. This result is used to give new proofs of two results of Eudave-Muñoz and Scharlemann's band sum theorem. | |
| dc.description | 43 pages, 12 figures; minor changes and corrections. Accepted by Pacific Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/0709.4051 | |
| dc.identifier | http://arxiv.org/abs/0709.4051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215844 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10; 57M50 | |
| dc.title | Boring split links | |
| dc.type | text |