Pseudo-Legendrian and Legendrian Simplicity of Links in 3-Manifolds
Abstract
We construct infinite families of non-simple isotopy classes of links in overtwisted contact structures on -bundles over surfaces. These examples include: (1) a pair of Legendrian links that are not Legendrian isotopic, but which are isotopic as framed links, homotopic as Legendrian immersed multi-curves, and have Legendrian-isotopic components and (2) a pair of Legendrian links that are not Legendrian isotopic, but are isotopic as framed links, homotopic as Legendrian immersed multi-curves, and which are link-homotopic as Legendrian links. Moreover, we construct examples showing that both of these non-simplicity phenomena can occur in the same smooth isotopy class. To construct these examples, we develop the theory of links transverse to a nowhere-zero vector field in a 3-manifold, and construct analogous examples in the category of links transverse to a vector field.
Keywords
Cite
@article{arxiv.2512.18185,
title = {Pseudo-Legendrian and Legendrian Simplicity of Links in 3-Manifolds},
author = {Patricia Cahn and Rima Chatterjee and Vladimir Chernov},
journal= {arXiv preprint arXiv:2512.18185},
year = {2026}
}
Comments
22 pages, 9 figures, minor typo corrected