K3#K3 上德恩扭转在单次稳定后的同伦
几何拓扑
2023-08-02 v6 代数拓扑
摘要
Kronheimer-Mrowka 最近证明了沿 颈部中一个 3-球面的德恩扭转不与恒等映射光滑同伦。这提供了 4-流形上自微分同胚的新例子：它们在拓扑范畴中与恒等映射同伦，但在光滑范畴中并非如此。（首个此类例子由 Ruberman 给出。）在本文中，我们利用 Pin(2)-等变 Bauer-Furuta 不变量证明，该德恩扭转即使在单次稳定（与 上的恒等映射做连通和）之后也不与恒等映射光滑同伦。这给出了单连通光滑 4-流形上 exotic 现象在单次稳定后不消失的首个例子。
引用
@article{arxiv.2003.03925,
title = {Isotopy of the Dehn twist on K3#K3 after a single stabilization},
author = {Jianfeng Lin},
journal= {arXiv preprint arXiv:2003.03925},
year = {2023}
}
备注
19 pages. Version 2:Added the reference to Gompf and Kreck's theorem and the reference to Szymik's work. Version 3: corrected several typos. Version 4: Added a few references. Version 5: corrected a few typos. Version 6: Final version, to appear in Geometry & Topology