群上左序空间上的拓扑
群论
2007-05-23 v2 几何拓扑
摘要
设 G 为一个群，令 O_G 表示 G 上左序的集合。则 O_G 可以自然方式赋予拓扑，我们将研究此拓扑以回答三个猜想。特别地，我们将证明 O_G 绝不可能为可数无穷。此外在 G 为可数非阿贝尔自由群的情形下，我们将证明 O_G 同胚于 Cantor 集，且 G 上左序的正锥非有限生成。对局部可指示群的推广也将被考虑。
引用
@article{arxiv.math/0607470,
title = {The topology on the space of left orderings of a group},
author = {Peter A. Linnell},
journal= {arXiv preprint arXiv:math/0607470},
year = {2007}
}
备注
This paper has been withdrawn. Adam S. Sikora has pointed out that the proof of Lemma 2.3 is wrong. It is not clear if the Lemma can be fixed. This doesn't affect Theorem 1.3, but does affect the other main results of the paper