PreprintCC BY-NC-ND 4.0HAL
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.
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BibTeX
@misc{barraud2026topological,
title = {{TOPOLOGICAL TRIVIALITY OF EXACT LAGRANGIAN COBORDISMS}},
author = {Jean-François J.-F. B. Barraud},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2611.03041},
eprint = {2611.03041},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05848642v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - TOPOLOGICAL TRIVIALITY OF EXACT LAGRANGIAN COBORDISMS
AU - Jean-François J.-F. B. Barraud
PY - 2026
DA - 2026/10/01
PB - HAL
DO - 10.48550/arxiv.2611.03041
UR - https://hal.science/hal-05848642v1
AB - 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.
ER -