An atlas of Legendrian knots
Symplectic Geometry
2013-05-08 v1 Geometric Topology
Abstract
We present an atlas of Legendrian knots in standard contact three-space. This gives a conjectural Legendrian classification for all knots with arc index at most 9, including alternating knots through 7 crossings and nonalternating knots through 9 crossings. Our method involves a computer search of grid diagrams and applies to transverse knots as well. The atlas incorporates a number of new, small examples of phenomena such as transverse nonsimplicity and non-maximal non-destabilizable Legendrian knots, and gives rise to new infinite families of transversely nonsimple knots.
Keywords
Cite
@article{arxiv.1010.3997,
title = {An atlas of Legendrian knots},
author = {Wutichai Chongchitmate and Lenhard Ng},
journal= {arXiv preprint arXiv:1010.3997},
year = {2013}
}
Comments
44 pages, including 25 pages of tables