接触拓扑中的凸超曲面理论
辛几何
2026-04-30 v4
摘要
我们建立了接触拓扑中凸超曲面理论的基础，推广了 Giroux 在三维情形下的工作。具体而言，我们证明接触流形中的任意闭超曲面均可被 逼近为一个凸超曲面。我们还证明，由 参数化的 泛型互不相交闭超曲面族除有限多个时刻 外均为凸的，且跨越每个 对应于一次 bypass 附着。作为一个应用，我们证明了接触流形存在相容的（相对）开书分解。
引用
@article{arxiv.1907.06025,
title = {Convex hypersurface theory in contact topology},
author = {Joseph Breen and Austin Christian and Ko Honda and Yang Huang},
journal= {arXiv preprint arXiv:1907.06025},
year = {2026}
}
备注
V4: Added two coauthors: Joseph Breen and Austin Christian; the part on contact submanifolds has been removed and will be written more carefully in a separate paper; the proof of the bypass-bifurcation correspondence has been expanded and the paper is now essentially self-contained with a 24-page appendix on bypasses in higher dimensions