关于在 3 维流形上按预定等值面重构 Morse 函数的条件
几何拓扑
2026-01-13 v3
摘要
我们讨论在 3 维流形上重构具有预定（正则）等值面的 Morse 函数的必要充分条件。本工作加强了作者先前仅研究充分条件的结果。我们的新工作也可视为一种附录。
引用
@article{arxiv.2412.20626,
title = {On reconstructing Morse functions with prescribed level sets on $3$-dimensional manifolds and a necessary and sufficient condition for the reconstruction},
author = {Naoki Kitazawa},
journal= {arXiv preprint arXiv:2412.20626},
year = {2026}
}
备注
10 pages. A kind of addenda to a published article http://mfat.imath.kiev.ua/article/?id=1911: here we show that the sufficient condition for reconstructing Morse functions there is also a necessary condition. This is submitted to another refereed journal motivated by the acceptance of the article [5] for publication