Classification of tangent and transverse knots in bracket-generating distributions

2022/10/02 by Javier Martínez-Aguinaga, Martínez-Aguinaga, Javier, Álvaro del Pino +1 · 1 citation
Mathematics · #57R22 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2210.00582

openalex publication_date 2022/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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