Legendrian knot and link atlases

On this page, there are links to atlases of Legendrian knots and two-component links of topological type with arc index at most 9. Various source files are also available. These files accompany the paper “An atlas of Legendrian knots” by Wutichai Chongchitmate and Lenhard Ng, arXiv:1010.3997. The work is based on Wutichai Chongchitmate's undergraduate senior thesis, which is also available below.

This page was last modified on 24 May 2011. For visitors who saw an earlier version of the knot atlas (from February 2010), the most recent version incorporates new data about transverse nonsimplicity derived from the transverse homology invariant.

The Legendrian knot atlas
This is the main atlas, with explanation, as a standalone file.

Atlas for Legendrian two-component links

Legend/explanation for the Legendrian two-component link atlas

Classification of Legendrian knots and links by Wutichai Chongchitmate: senior thesis, Duke University, 2010

Source files:

• atlas-code.tar: The Java code (in preliminary form) used to produce the Legendrian knot atlas.
• XO Permutation.pdf, XO Permutation.tex: a table of the grid diagrams depicted in the knot atlas, represented by their X-O data. For knots with multiple grid diagrams, the order of the grid diagrams agrees with the order that they appear in the knot atlas.
• braid presentation.pdf, braid presentation.tex: a table of the Legendrian knots corresponding to the grid diagrams in the knot atlas, expressed as plat closures of braids. This may be useful for input into the Mathematica program “Legendrian invariants.nb”, available here, which computes various Legendrian knot invariants. Note: for starred knot types, plat presentations are not guaranteed to appear in the order that the corresponding grid diagrams appear in the atlas.

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