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 ℝ2n+1. We show that these three constructions are isotopic (whenever defined). We also recover and generalise a result of Courte and Ekholm, that shows Ekholm’s doubling procedure produces the standard Legendrian unknot.

Link to arxiv