Math @ Duke
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Publications [#243947] of Lenhard L. Ng
Papers Published
- Chongchitmate, W; Ng, L, An atlas of Legendrian knots,
Experimental Mathematics, vol. 22 no. 1
(2011),
pp. 26-37, Informa UK Limited [arXiv:1010.3997], [doi]
(last updated on 2024/03/28)
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 seven crossings and nonalternating knots through nine 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 nonmaximal nondestabilizable Legendrian knots, and gives rise to new infinite families of transversely nonsimple knots. © 2013 Copyright Taylor and Francis Group, LLC.
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