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Constructions and Isotopies of High-Dimensional Legendrian Spheres (2211.00773v2)
Published 1 Nov 2022 in math.SG and math.GT
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 $\mathbb{R}{2n+1}$. 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.
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