辛流形的 PL 逼近
微分几何
2024-06-27 v2
摘要
本文是对分段线性（PL）辛拓扑学的贡献。我们定义 PL 辛流形为赋予分段常值 Whitney 辛形式的组合流形，并探究这两类辛空间之间可能的关系。我们证明光滑辛流形容许关于辛形式处于一般位置的任意精细的光滑三角剖分，且可被 PL 辛流形 -逼近。除平凡情形外，我们无法证明光滑辛结构可被三角剖分，但可证明它们相伴的体积形式能被某些此类逼近 PL 流形的体积形式所三角剖分。
引用
@article{arxiv.2112.10118,
title = {PL approximations of symplectic manifolds},
author = {Mélanie Bertelson and Julie Distexhe},
journal= {arXiv preprint arXiv:2112.10118},
year = {2024}
}
备注
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