Some groups of type VF

• 成果类型: Article
• 署名作者: Leary, IJ; Nucinkis, BEA
• 署名单位: University of Southampton; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-002-0254-7
• 发表日期: 2003
• 页码: 135-165
• 关键词: fixed-point theorem; finiteness properties; K-THEORY; classifying space; assembly maps; SUBGROUPS; characters; HOMOLOGY; sets

摘要

A group is of type VF if-it hag a finite-index subgroup which has a finite classifying space. We construct groups of type VF in which the centralizers of some elements of finite order are not of type VF and groups of type VF containing infinitely many conjugacy classes of finite subgroups. It follows that a group G of type VF need not admit a finite-type universal proper G-space. We construct groups G for which the minimal dimension of a universal proper G-space is strictly greater than the virtual cohomological dimension of G. Each of our groups embeds in GL(m) (Z) for sufficiently large m. Some applications to K-theory are also considered.