Periodic Complexes and Group Actions

Details Periodic Complexes and Group Actions Periodic Complexes and Group Actions

2000-10-10

arxiv.org/abs/math/0010096v2

Mathematics

Algebraic Topology

Revised version

Scientific paper

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 an orientable spherical fibration with total space that is homotopically finite dimensional. As applications we characterize those discrete groups that act freely and properly on a cartesian product of euclidean space and a sphere; we construct non-standard free actions of rank two simple groups on finite complexes Y homotopy equivalent to a product of two spheres 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 X Z/p X Z/p.

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