Regular Lagrangians are smooth Lagrangians
Symplectic Geometry
2025-04-22 v2 Algebraic Topology
Category Theory
Abstract
We prove that for any element in the -completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its -support is a smooth Lagrangian submanifold, then the element itself is a smooth Lagrangian. We also prove that if the -support of an element in the completion is compact, then it is connected.
Cite
@article{arxiv.2407.00395,
title = {Regular Lagrangians are smooth Lagrangians},
author = {Tomohiro Asano and Stéphane Guillermou and Yuichi Ike and Claude Viterbo},
journal= {arXiv preprint arXiv:2407.00395},
year = {2025}
}
Comments
16 pages, 2 figures. v2: Revised, to appear in J. Math. Soc. Japan