Approximability for Lagrangian submanifolds
Symplectic Geometry
2026-01-21 v1 Algebraic Topology
Differential Geometry
Abstract
This paper introduces a notion of categorical approximability for metric spaces that can be viewed as a categorification of approximability for metric groups, as defined by Turing in 1938. Approximability as introduced here is a property of metric spaces that is more general than precompactness. It is shown that several classes of Lagrangian submanifolds - closed Lagrangian submanifolds in a cotangent disk bundle; equators on the sphere; weakly exact Lagrangians on the torus-endowed with the spectral metric are approximable in this sense. Among other geometric applications, we show that there are such examples of spaces of Lagrangians that are approximable but are not precompact.
Cite
@article{arxiv.2601.12506,
title = {Approximability for Lagrangian submanifolds},
author = {Giovanni Ambrosioni and Paul Biran and Octav Cornea},
journal= {arXiv preprint arXiv:2601.12506},
year = {2026}
}
Comments
155 pages, 13 figures