粗 Cartan-Hadamard 定理及其在粗 Baum-Connes 猜想中的应用
度量几何
2021-04-01 v3 K理论与同调
摘要
我们建立了 Cartan-Hadamard 定理的一个粗版本，该定理表明适当的粗凸空间与其理想边界的开锥粗同伦等价。作为一个应用，我们证明了此类空间满足粗 Baum-Connes 猜想。结合 Osajda-Przytycki 的结果，它意味着收缩群与局部有限收缩复形满足粗 Baum-Connes 猜想。
引用
@article{arxiv.1705.05588,
title = {A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture},
author = {Tomohiro Fukaya and Shin-ichi Oguni},
journal= {arXiv preprint arXiv:1705.05588},
year = {2021}
}
备注
v.2 34 pages, added Section 7 on groups acting on a coarsely convex space. v.3 38 pages, added Section 8 on a functional analytic characterization of ideal boundaries