Periodic complexes and group actions

• 成果类型: Article
• 署名作者: Adem, A; Smith, JH
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062102
• 发表日期: 2001
• 页码: 407-435
• 关键词: equivariant cohomology; projective-resolutions; spheres

摘要

In this paper we show that the cohomology of a connected CW-complex is periodic if and only if it is the base space of a spherical fibration with total space that is homotopically finite dimensional. As applications we characterize those discrete groups that act freely and properly on R-n x S-m; we construct nonstandard free actions of rank-two simple groups on finite complexes Y similar or equal to S-n x S-m; and we prove that a finite p-group P acts freely on such a complex if and only if it does not contain a subgroup isomorphic to (Z/p)(3).