= Homotopy groups of the stunted projective space through degree nine
{title2=$\pi_7(\mathbb{RP}^{10}/\mathbb{RP}^6)=\pi_9(\mathbb{RP}^{10}/\mathbb{RP}^6)=\mathbb Z/2$}
For this quotient, homotopy groups through degree six and in degree eight vanish. The degree-seven and degree-nine groups are $\mathbb Z/2$. A map to $K(\mathbb Z/2,7)$ induces an isomorphism on degree-nine integral <homology> because the relevant square of the bottom mod-two class is nonzero. Two relative Hurewicz steps then compute degrees eight and nine.
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