Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra

Abstract. 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 be-tween 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 exis-tence 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. 1