关于具有正的第一$\ell^2$-Betti数的群的锥双曲性
群论
2018-05-16 v2 几何拓扑
算子代数
摘要
我们证明，每个具有正的第一-Betti数且虚拟满射到 的有限呈现群都是锥双曲的。特别地，这蕴含了具有正的第一-Betti数的有限呈现剩余有限群以及亏数至少为 的群的锥双曲性。
引用
@article{arxiv.1501.03066,
title = {On acylindrical hyperbolicity of groups with positive first $\ell^2$-Betti number},
author = {D. Osin},
journal= {arXiv preprint arXiv:1501.03066},
year = {2018}
}
备注
The published version of this paper used a result from arXiv:1310.6289 whose proof contained a gap. The gap and necessary changes to the published version of this paper are discussed in arXiv:1711.09486. This version incorporates these changes