The Morava \(K\)-Theory Eilenberg-Moore spectral sequence (Q958352)

The author considers the convergence of the Eilenberg--Moore spectral sequence in Morava \(K\)-theory for the fibration \[ \Omega B \to PB \to B, \] where \(\Omega B\) and \(PB\) are the loop space and path space of~\(B\). He shows that the spectral sequence converges to the Morava \(K\)-theory of \(\Omega B\) if the Eilenberg--Moore spectral sequence for ordinary homology collapses and if certain finiteness conditions are satisfied.