Classification of tangent and transverse knots in bracket-generating distributions

Abstract

Consider a manifold, of dimension greater than 3, equipped with a bracket-generating distribution. In this article we prove complete h-principles for embedded regular horizontal curves and for embedded transverse curves. These results contrast with the 3-dimensional contact case, where the full h-principle for transverse/legendrian knots is known not to hold. We also prove analogous statements for immersions, with no assumptions on the ambient dimension.