A POLYNOMIAL MODEL FOR THE DOUBLE-LOOP SPACE OF AN EVEN SPHERE - Kamiyama, Yasuhiko (Proceedings of the Edinburgh Mathematical Society, 2004)
It is well known that $\varOmega^2S^{2n+1}$ is approximated by $Rat_{k}(\mathbb{C}P^{n})$, the space of based holomorphic maps of degree $k$ from $S^2$ to $\mathbb{C}P^{n}$. In this paper we construct a space $G_{k}^{n}$ which is an analogue of $Rat_{k}(\mathbb{C}P^{n})$, and prove that under the natural map $j_k:G_{k}^{n}→\varOmega^2S^{2n}$, $G_{k}^{n}$ approximates $\varOmega^2S^{2n}$. AMS 2000 Mathematics subject classification: Primary 55P35