I am trying to compute the cohomology of the homotopy fibre $F$ of a continuous map $f \colon S^{2n-1} \to S^n$ ($n$ even and non-zero Hopf invariant). It is easy to see that through the Serre spectral sequence the non zero groups are (with integer coefficients) $$ H^{n-1}(F) = \mathbb Z,\quad H^k(F) = \mathbb Z_m $$ for $k = 2n-1 + j(n-1)$ and $j=0,1,2,\dots$ ($m=1$ means here that all that the latter groups are all zero). Someone mentioned to me that $m$ is just the Hopf-invariant of $f$. He didnt had a proof and I can not show or see this.