Quasi-isometry invariance of group splittings

• 成果类型: Article
• 署名作者: Papasoglu, P
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.161.759
• 发表日期: 2005
• 页码: 759-830
• 关键词: convergence groups

摘要

We show that a finitely presented one-ended group which is not commensurable to a surface group splits over a two-ended group if and only if its Cayley graph is separated by a quasi-line. This shows in particular that splittings over two-ended groups are preserved by quasi-isometries.