[For the entire collection see Zbl 0699.00032.] A fibration $F\to E\to B$ is called totally noncohomologuous to zero (TNCZ) with respect to the coefficient field k, if $H^{*}(E;k)\to H^{*}(F;k)$ is surjective. This is equivalent to saying that ${\pi }_1\left(B\right)$ acts trivially on $H^{*}(F;k)$ and the Serre spectral sequence collapses at $E^2$. S. Halperin conjectured that for $char\left(k\right)=0$ and F a 1-connected rationally elliptic space (i.e., both $H^{*}(F;𝒬)$ and ${\pi }_{*}\left(F\right)\otimes 𝒬$ are finite dimensional) such that $H^{*}(F;k)$ vanishes in odd degrees, every fibration $F\to E\to B$ is TNCZ. The author proves this being the case...

For the entire collection see Zbl 0699.00032.