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September 2004 Legendrian solid-torus links
Lenhard Ng
J. Symplectic Geom. 2(3): 411-443 (September 2004).


Differential graded algebra invariants are constructed for Legendrian links in the $1$-jet space of the circle. In parallel to the theory for $\R^3$, Poincar\'e--Chekanov polynomials and characteristic algebras can be associated to such links. The theory is applied to distinguish various knots, as well as links that are closures of Legendrian versions of rational tangles. For a large number of two-component links, the Poincar\'e--Chekanov polynomials agree with the polynomials defined through the theory of generating functions. Examples are given of knots and links which differ by an even number of horizontal flypes that have the same polynomials but distinct characteristic algebras. Results obtainable from a Legendrian satellite construction are compared to results obtainable from the DGA and generating function techniques.


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Lenhard Ng. "Legendrian solid-torus links." J. Symplectic Geom. 2 (3) 411 - 443, September 2004.


Published: September 2004
First available in Project Euclid: 14 June 2005

zbMATH: 1097.57014
MathSciNet: MR2131643

Rights: Copyright © 2004 International Press of Boston


Vol.2 • No. 3 • September 2004
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