Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra

Published

Journal Article

We develop a close relation between satellites of Legendrian knots in ℝ3 and the Chekanov-Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence between rulings of a Legendrian knot in ℝ3 and augmentations of its DGA by showing that the DGA has finite-dimensional representations if and only if there exist certain rulings of satellites of the knot. We derive several consequences of this result, notably that the question of existence of ungraded finite-dimensional representations for the DGA of a Legendrian knot depends only on the topological type and Thurston-Bennequin number of the knot.

Full Text

Duke Authors

Cited Authors

  • Ng, L; Rutherford, D

Published Date

  • August 1, 2013

Published In

Volume / Issue

  • 13 / 5

Start / End Page

  • 3047 - 3097

Electronic International Standard Serial Number (EISSN)

  • 1472-2739

International Standard Serial Number (ISSN)

  • 1472-2747

Digital Object Identifier (DOI)

  • 10.2140/agt.2013.13.3047

Citation Source

  • Scopus