|
|||||
|
|
|
|
|
|
|
|
|
Legendrian and transverse
cables of positive torus knots
John B Etnyre, Douglas J LaFountain and Bülent Tosun |
|
Geometry & Topology 16 (2012) 1639–1689
|
Abstract |
|
We classify Legendrian and transverse knots in the knot types obtained from positive torus knots by cabling. This classification allows us to demonstrate several new phenomena. Specifically, we show there are knot types that have nondestabilizable Legendrian representatives whose Thurston–Bennequin invariant is arbitrarily far from maximal. We also exhibit Legendrian knots requiring arbitrarily many stabilizations before they become Legendrian isotopic. Similar new phenomena are observed for transverse knots. To achieve these results we define and study “partially thickenable” tori, which allow us to completely classify solid tori representing positive torus knots. |
Keywords
Legendrian, contact, cable, torus knot
|
Mathematical Subject Classification 2010
Primary: 53D10, 57R17
Secondary: 57M50
|
References |
Publication
Received: 6 May 2011
Revised: 3 March 2012
Accepted: 5 June 2012
Published: 3 August 2012
Proposed: Yasha Eliashberg
Seconded: Peter S Ozsváth, Ronald J Stern
|
Authors |
| John B Etnyre | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta GA 30332-0160 USA |
|
| http://www.math.gatech.edu/~etnyre | |
| Douglas J LaFountain | |
| Centre for Quantum Geometry of
Moduli Spaces Aarhus University Ny Munkegade 118 DK-8000 Aarhus C Denmark |
|
| Bülent Tosun | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta GA 30332-0160 USA |
|
| http://www.math.gatech.edu/users/btosun3 | |
|
