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2006 Generating family invariants for Legendrian links of unknots
Jill Jordan, Lisa Traynor
Algebr. Geom. Topol. 6(2): 895-933 (2006). DOI: 10.2140/agt.2006.6.895

Abstract

Theory is developed for linear-quadratic at infinity generating families for Legendrian knots in 3. It is shown that the unknot with maximal Thurston–Bennequin invariant of 1 has a unique linear-quadratic at infinity generating family, up to fiber-preserving diffeomorphism and stabilization. From this, invariant generating family polynomials are constructed for 2–component Legendrian links where each component is a maximal unknot. Techniques are developed to compute these polynomials, and computations are done for two families of Legendrian links: rational links and twist links. The polynomials allow one to show that some topologically equivalent links with the same classical invariants are not Legendrian equivalent. It is also shown that for these families of links the generating family polynomials agree with the polynomials arising from a linearization of the differential graded algebra associated to the links.

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Jill Jordan. Lisa Traynor. "Generating family invariants for Legendrian links of unknots." Algebr. Geom. Topol. 6 (2) 895 - 933, 2006. https://doi.org/10.2140/agt.2006.6.895

Information

Received: 28 March 2006; Accepted: 25 April 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1130.57018
MathSciNet: MR2240920
Digital Object Identifier: 10.2140/agt.2006.6.895

Subjects:
Primary: 53D10
Secondary: 57M25

Rights: Copyright © 2006 Mathematical Sciences Publishers

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