= Minimal model of the fibre of the projective-space collapse map
For a degree-one map $f:\mathbb{CP}^n\to S^{2n}$ with $n\ge2$, a <minimal model> of its <homotopy fibre> is $(\Lambda(x_2,a_{2n-1},z_{2n+1},b_{4n-2}),d)$ with $dx=dz=0$, $da=x^n$, $db=x^{n-1}z$. Adjoin suspended sphere generators to the projective-space model to model the path pullback, then put $z=y-xa$; the differential becomes the displayed decomposable one. The <rational homotopy groups> are one-dimensional in those four generator degrees and zero otherwise. At $n=1$ the map is a <rational homotopy equivalence> and the minimal fibre model is $\mathbb Q$.
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