A transfer spectral sequence for fixed point free involutions with an application to stunted real projective spaces (Q1060747)

The author shows: If X is a finite CW complex admitting a fixed point free involution then there is a singly graded spectral sequence with \(E^*_ 1=H^*(X,{\mathbb{Z}}_ 2)\) and \(E^*_{\infty}=0\). And, for any \(n>0\) there exists k(n) such that if \(n>k(n)\) and X is a homotopy \({\mathbb{R}}P^{n+k}/{\mathbb{R}}P^ n\), then X will not admit a fixed point free involution.