自由乘自由与曲面乘自由群的不相干性
群论
2021-10-05 v3 几何拓扑
摘要
设为半直积，其中为自由群（）或亏格的闭曲面的基本群。我们证明是不相干的，解决了D. Wise提出的两个问题。这给出了J. Hillman关于曲面上的曲面丛的基本群问题的肯定回答。尽管许多群已被利用虚代数纤维性证明为不相干，我们也证明并非每个自由乘自由群都虚代数纤维。
引用
@article{arxiv.2005.01202,
title = {Incoherence of free-by-free and surface-by-free groups},
author = {Robert Kropholler and Stefano Vidussi and Genevieve Walsh},
journal= {arXiv preprint arXiv:2005.01202},
year = {2021}
}
备注
There is an error in the proofs of Theorem 3.1 and Theorem 3.5 which we cannot immediately fix. We thank Hongbin Sun for pointing this error out. We are merging the results on groups which do not virtually algebraically fiber (which are unaffected by this error) with our paper arXiv:2103.06930