Periodic complexes and group actions

By A. Adem, Jeffrey H. Smith. 2000

96 citations recorded by the source corpus.

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 In x Sm; we construct nonstandard free actions of rank-two simple groups on finite complexes Y Sn x Sm; 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cfbefc1d740777fe06ac10866f92d753510bbada

How researchers see this paper

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In Geometry and Topology

1. Albert Ruiz
2. Antonio Viruel
3. Antonio Díaz

In Mathematical Physics

1. Albert Ruiz
2. Antonio Viruel
3. Antonio Díaz

Citations in the corpus

• All p-local finite groups of rank two for odd prime p (2004, background): “when constructing actions on spheres [2, 1]) or modular representation theory (e.”