Let \(n\ge2\). Prove that there do not exist an integer \(k\) and a space \(X\) such that \[ \mathbb{CP}^n\simeq S^k\vee X. \]
Complex projective space does not split off a sphere wedge
P-QUAL-REVIEW-HATCHER-14
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P-QUAL-REVIEW-HATCHER-14
Let \(n\ge2\). Prove that there do not exist an integer \(k\) and a space \(X\) such that \[ \mathbb{CP}^n\simeq S^k\vee X. \]