Legendrian submanifolds with hamiltonian isotopic symplectizations

TL;DR

This paper constructs examples of Legendrian submanifolds in high-dimensional contact manifolds whose Lagrangian cylinders in the symplectization are Hamiltonian isotopic, despite the submanifolds not being diffeomorphic.

Contribution

It provides explicit examples of Legendrian submanifolds with Hamiltonian isotopic symplectizations that are not diffeomorphic, revealing new phenomena in high-dimensional contact topology.

Findings

Existence of non-diffeomorphic Legendrian submanifolds with Hamiltonian isotopic Lagrangian cylinders

Construction methods for Legendrian submanifolds in contact manifolds of dimension ≥11

Insights into the relationship between Legendrian submanifolds and their symplectizations

Abstract

In any contact manifold of dimension $2n-1\geq 11$, we construct examples of closed legendrian submanifolds which are not diffeomorphic but whose lagrangian cylinders in the symplectization are hamiltonian isotopic.