Some examples in the integral and Brown-Peterson cohomology of p-groups
Abstract
Description
For each odd prime p, we exhibit p-groups G of p-rank two such that (suitably defined) Chern classes of unitary representations of G fail to generate the following rings:
1. The even degree integral cohomology of G;
2. The final page of the Atiyah-Hirzebruch spectral sequence for G;
3. The Brown-Peterson generalized cohomology of G.
It follows that these groups afford counterexamples to conjectures of C. B. Thomas, M. F. Atiyah and P. Landweber.