PL approximations of symplectic manifolds
Abstract
This paper is a contribution to piecewise linear (PL) symplectic topology. We define the notion of PL symplectic manifold as being a combinatorial manifold endowed with a piecewise constant Whitney symplectic form and investigate possible relations between the two categories of symplectic spaces. We prove that smooth symplectic manifolds admit arbitrarily fine smooth triangulations in general position with respect to the symplectic form and can be -approximated by PL symplectic manifolds. We cannot prove that smooth symplectic structures can be triangulated, except in trivial cases, but we can prove that their associated volume form can be triangulated by the volume form of some of these approximating PL manifolds.
Keywords
Cite
@article{arxiv.2112.10118,
title = {PL approximations of symplectic manifolds},
author = {Mélanie Bertelson and Julie Distexhe},
journal= {arXiv preprint arXiv:2112.10118},
year = {2024}
}
Comments
35 pages, 4 figures. This paper is an extension of the previous version that contains a symplectic jiggling lemma in addition to the triangulation of volume forms and a proof that smooth symplectic manifolds can be approximated by PL ones. It has been accepted for publication in the Journal of Symplectic Geometry