Volume 6, issue 2 (2006)

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

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

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
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Generating family invariants for Legendrian links of unknots

Jill Jordan and Lisa Traynor

Algebraic & Geometric Topology 6 (2006) 895–933

arXiv: 0904.2690


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.

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