2012/06/11 by Lenhard Ng, Dan Rutherford · 1 citation
Mathematics · #math.SG #math.GT #msc:57R17 #msc:53D42 #msc:57M25
paper · pdf · doi:10.2140/agt.2013.13.3047
published as Algebr. Geom. Topol. 13 (2013) 3047-3097 · 43 pages
arxiv created 2012/06/11 · arxiv updated 2013/08/13
We study satellites of Legendrian knots in R3 and their relation to 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.