Group cocycles and the ring of affiliated operators

• 成果类型: Article
• 署名作者: Peterson, Jesse; Thom, Andreas
• 署名单位: Leipzig University; Vanderbilt University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0310-2
• 发表日期: 2011
• 页码: 561-592
• 关键词: finitely generated subgroups; w-rigid groups; malleable actions; group cohomology; limit groups; ii1 factors; l2-cohomology; equivalent

摘要

In this article we study cocycles of discrete countable groups with values in l(2)G and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in l(2)G and answer several questions from De Cornulier et al. (Transform. Groups 13(1): 125-147, 2008). Moreover, we obtain strong results about the existence of free subgroups and the subgroup structure, provided the group has a positive first l(2)-Betti number. We give numerous applications and examples of groups which satisfy our assumptions.