Exact Lagrangian cobordism and pseudo-isotopy

TL;DR

This paper proves that under certain conditions, an exact Lagrangian cobordism of dimension greater than five is a Lagrangian pseudo-isotopy, advancing understanding of their topological and symplectic properties.

Contribution

It demonstrates that, assuming specific topological conditions, exact Lagrangian cobordisms are equivalent to Lagrangian pseudo-isotopies, providing a partial validation of a conjecture by Biran and Cornea.

Findings

Exact Lagrangian cobordisms of dimension >5 are Lagrangian pseudo-isotopies under certain assumptions.

Supports a weaker form of the conjecture relating cobordisms to Hamiltonian isotopies.

Advances the classification of Lagrangian cobordisms in high dimensions.

Abstract

We show that under some topological assumptions, an exact Lagrangian cobordism $(W; L_{0}, L_{1})$ of dimension $dim(W) >5$ is a Lagrangian pseudo-isotopy. This result is a weaker form of a conjecture proposed by Biran and Cornea, which states that any exact Lagrangian cobordism is Hamiltonian isotopic to a Lagrangian suspension.