Classification of tangent and transverse knots in bracket-generating distributions

Javier Martínez-Aguinaga; Álvaro del Pino

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arXiv · 2210.00582

Classification of tangent and transverse knots in bracket-generating distributions

Javier Martínez-Aguinaga·Álvaro del Pino

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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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Javier Martínez-Aguinaga, Álvaro del Pino. 2022-10-02. Classification of tangent and transverse knots in bracket-generating distributions. https://arxiv.org/abs/2210.00582

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