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arXiv · 2611.03041

Topological triviality of exact Lagrangian Cobordisms

Jean-François Barraud
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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.

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Jean-François Barraud. 2026-11-02. Topological triviality of exact Lagrangian Cobordisms. https://arxiv.org/abs/2611.03041

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