An atlas of Legendrian knots

Details An atlas of Legendrian knots An atlas of Legendrian knots

2010-10-19

arxiv.org/abs/1010.3997v1

Mathematics

Symplectic Geometry

44 pages, including 25 pages of tables

Scientific paper

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.

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