On transversally simple knots
| dc.creator | Birman, Joan S. | |
| dc.creator | Wrinkle, Nancy C. | |
| dc.date | 1999-10-29 | |
| dc.date | 2001-04-11 | |
| dc.date.accessioned | 2026-07-07T05:31:21Z | |
| dc.date.available | 2026-07-07T05:31:21Z | |
| dc.description | Final revision. To appear in the Journal of Differential Geometry. This paper studies knots that are transversal to the standard contact structure in $\reals^3$, bringing techniques from topological knot theory to bear on their transversal classification. We say that a transversal knot type $\cTK$ is {\it transversally simple} if it is determined by its topological knot type $\cK$ and its Bennequin number. The main theorem asserts that any $\cTK$ whose associated $\cK$ satisfies a condition that we call {\em exchange reducibility} is transversally simple. As a first application, we prove that the unlink is transversally simple, extending the main theorem in \cite{El}. As a second application we use a new theorem of Menasco (Theorem 1 of \cite{Me}) to extend a result of Etnyre \cite{Et} to prove that iterated torus knots are transversally simple. We also give a formula for their maximum Bennequin number. We show that the concept of exchange reducibility is the simplest of the constraints that one can place on $\cK$ in order to prove that any associated $\cTK$ is transversally simple. We also give examples of pairs of transversal knots that we conjecture are {\em not} transversally simple. | |
| dc.description | 28 pages, 17 figures. Final revision includes a formula for computing the maximum Bennequin number for an iterated torus knot. Accepted for publication in Journal of Differential Geometry | |
| dc.identifier | https://arxiv.org/abs/math/9910170 | |
| dc.identifier | http://arxiv.org/abs/math/9910170 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79309 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | On transversally simple knots | |
| dc.type | text |