A closed oriented manifold M with the fundamental group G is called Q-inessential if the classifying map M –> BG sends to zero the fundamental class of M with rational coefficients. We prove that if M is Q-inessential, then the Hofer-Zehnder capacity of the unit disk bundle of the cotangent bundle of M is finite. The proof uses the classical Goodwillie's theory of homology of loop spaces, and a recent theorem of K. Irie about spectral invariants and Hofer-Zehnder capacities.
This is a joint work with Urs Frauenfelder.
Update : April 22, 2016