A bound on the exponent of the cohomology of BC-bundles

Details A bound on the exponent of the cohomology of BC-bundles A bound on the exponent of the cohomology of BC-bundles

2007-11-30

arxiv.org/abs/0711.5007v1

Proceedings of the 1994 Barcelona Conference on Algebraic Topology, Progress in Mathematics 136, Birkhaeuser (1996) 255-260

Mathematics

Algebraic Topology

Scientific paper

We give a lower bound for the exponent of certain elements in the integral cohomology of the total spaces of principal BC-bundles for C a finite cyclic group. As applications we give a proof of the theorem of A. Adem and H.-W. Henn that a p-group is elementary abelian if and only if its integral cohomology has exponent p, and we exhibit some infinite groups of finite virtual cohomological dimension whose Tate-Farrell cohomology contains torsion of order greater than the l.c.m. of the orders of their finite subgroups. We also give an upper bound for the exponent of all but finitely many of the integral cohomology groups of a finite group, in terms of the permutation representations of the group.

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