Constructions and Isotopies of High-Dimensional Legendrian Spheres
Symplectic Geometry
2025-06-25 v2 Geometric Topology
Abstract
We explore the construction of Legendrian spheres in contact manifolds of any dimension. Two constructions involving open books work in any contact manifold, while one introduced by Ekholm works only in . We show that these three constructions are isotopic to the Legendrian unknot, thus recovering and generalising a result of Courte and Ekholm, that shows Ekholm's doubling procedure produces the standard Legendrian unknot.
Cite
@article{arxiv.2211.00773,
title = {Constructions and Isotopies of High-Dimensional Legendrian Spheres},
author = {Agniva Roy},
journal= {arXiv preprint arXiv:2211.00773},
year = {2025}
}
Comments
15 pages, 9 figures. Significant rewrites following referee feedback. Discarded section on stabilization as surgery and simplified proof of main theorem