Volume 6, issue 2 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Generating family invariants for Legendrian links of unknots

Jill Jordan and Lisa Traynor

Algebraic & Geometric Topology 6 (2006) 895–933

arXiv: 0904.2690

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.

Keywords
Legendrian links, generating functions, generating families, DGA
Mathematical Subject Classification 2000
Primary: 53D10
Secondary: 57M25
References
Forward citations
Publication
Received: 28 March 2006
Accepted: 25 April 2006
Published: 24 July 2006
Authors
Jill Jordan
Department of Mathematics
Bryn Mawr College
Bryn Mawr PA 19010
USA
Lisa Traynor
Department of Mathematics
Bryn Mawr College
Bryn Mawr PA 19010
USA