Classification of tangent and transverse knots in bracket-generating distributions
Differential Geometry
2022-10-04 v1
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.
Keywords
Cite
@article{arxiv.2210.00582,
title = {Classification of tangent and transverse knots in bracket-generating distributions},
author = {Javier Martínez-Aguinaga and Álvaro del Pino},
journal= {arXiv preprint arXiv:2210.00582},
year = {2022}
}
Comments
Preliminary version