An atlas of Legendrian knots


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Chongchitmate, W; Ng, L

Published Date

  • January 1, 2013

Published In

Volume / Issue

  • 22 / 1

Start / End Page

  • 26 - 37

Electronic International Standard Serial Number (EISSN)

  • 1944-950X

International Standard Serial Number (ISSN)

  • 1058-6458

Digital Object Identifier (DOI)

  • 10.1080/10586458.2013.750221

Citation Source

  • Scopus