The complex affine quadric $Q^{ m}=\{ z\in { \Bbb C}^{ m+1}\mid z_{ 1}^{ 2}+...+z_{ m+1}^{ 2}=1\}$ deforms by retraction onto $S^{ m}$; this allows us to identify $[Q^{ k},Q^{ n}]$ and $[S^{ k},S^{ n}]=\pi_{ k}(S^{ n})$. Thus one will say that an element of $\pi_{ k}(S^{ n})$ is complex representable if there exists a complex polynomial map from $Q^{ k}$ to $Q^{ n}$ corresponding to this class. In this Note we show that $\pi_{ n+1}(S^{ n})$ and $\pi_{ n+2}(S^{ n})$ are complex representable.
Categories: math.AT