Ran Levi

Northwestern University (previous, University of Heidelberg)
 

On Homological rate of Growth and the Homotopy type of \Omega BG^p


Let G be a finite p-perfect group. We show that the mod-p homology of
\Omega BG^p grows either polynomially or semi-exponentially. A
conjecture due to F. Cohen states that  \Omega BG^p for such groups G
is spherically  resolvable of finite weight. We show that any space X,
which satisfies the conclusion of Cohen's conjecture has the property
that   its homology grows at most hyper-polynomially of finite
degree. Thus we conclude that if a group $G$  satisfies the Cohen
conjecture then the homology of \Omega BG^p  grows polynomially. This
enable us to produce  counter examples to the conjecture. We study
some further homotopy properties of our  examples. We also show that
the mod p homology of \Omega BG^p is a finitely generated, Lie nilpotent
algebra  provided it grows polynomially. 

Preprint