Topological triviality of exact Lagrangian Cobordisms

Abstract

Inspired by the rigidity of exact Lagrangian submanifolds, a conjecture by P.~Biran and O.~Cornea asks if a simple exact Lagrangian cobordism $W$ in a tame exact symplectic manifold is always ``symplectically trivial'' (i.e. the Lagrangian suspension of an Hamiltonian isotopy). In this short note, we prove a topological version of this conjecture~: if the cobordism has dimension at least $6$, it is always topologically trivial. This extends a previous work of Lara Suarez who reduced the question to proving an injectivity result among fundamental groups.