Complex Polynomial Representation of ${\pi }_{n+1}(s^n)$ and ${\pi }_{n+2}(s^n)$

Francisco-Javier Turiel

The complex affine quadric $Q^m=\{z\in {\mathbb{C}}^{m+1}\mid z_1^2+...+z_{m+1}^2=1\}$ deforms by retraction onto $S^m$; this allows us to identify $[Q^k,Q^n]$ and $[S^{k…