系数在一致凸 Banach 空间中的有界上同调
群论
2015-02-16 v2 几何拓扑
摘要
我们证明：对于无平凡有限正规子群的 acylindrically hyperbolic 群 ，以及 在（非零）一致凸 Banach 空间中的任意酉表示 ，向量空间 是无限维的。该结果此前已知适用于 上的正则表示（），但论证方法不同。然而，即使在非阿贝尔自由群的情形下，我们的结果在如此广泛的表示类中也是新的；此外，acylindrically hyperbolic 群的情形可作为推论得出。
引用
@article{arxiv.1306.1542,
title = {Bounded cohomology with coefficients in uniformly convex Banach spaces},
author = {Mladen Bestvina and Ken Bromberg and Koji Fujiwara},
journal= {arXiv preprint arXiv:1306.1542},
year = {2015}
}
备注
The title has been changed. The old title was "Bounded cohomology via quasi-trees". We prove a theorem for free groups (Theorem 1.1) using actions on trees, then deal with acylindrically hyperbolic groups using a work by Hull-Osin (Corollary 1.2). In the old version we had a direct proof using quasi-trees. We move the discussion on strongly contracting geodesics to a separate paper ([3])