Generating family invariants for Legendrian links of unknots

Abstract

Theory is developed for linear-quadratic at infinity generating families for Legendrian knots in R^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.

arXiv commentThis is the version published by Algebraic & Geometric Topology on 24 July 2006

References in corpus (1)

• Generating function polynomials for legendrian links

Cited by in corpus (11)

• Generating families and Legendrian contact homology in the standard contact space
• Lagrangian Cobordisms via Generating Families: Constructions and Geography
• Contact Homology, Capacity and Non-Squeezing in R^2n x S^1 via Generating Functions
• Obstructions to Lagrangian Cobordisms between Legendrians via Generating Families
• A combinatorial DGA for Legendrian knots from generating families
• Connections between Floer-type invariants and Morse-type invariants of Legendrian knots
• Equivalence classes of augmentations and Morse complex sequences of Legendrian knots
• Generating families and constructible sheaves
• Topologically Distinct Lagrangian and Symplectic Fillings
• Obstructions to the Existence and Squeezing of Lagrangian Cobordisms
• A product structure on Generating Family Cohomology for Legendrian Submanifolds