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even sphere

Proceedings of the Edinburgh Mathematical Society (1)

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A POLYNOMIAL MODEL FOR THE DOUBLE-LOOP SPACE OF AN EVEN SPHERE
Yasuhiko Kamiyama
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 47 / Issue 1 / February 2004

Published online by Cambridge University Press:

27 May 2004, pp. 155-162
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It is well known that $\varOmega^2S^{2n+1}$ is approximated by $\textrm{Rat}_{k}(\mathbb{C}P^{n})$, 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 $\textrm{Rat}_{k}(\mathbb{C}P^{n})$, and prove that under the natural map $j_k:G_{k}^{n}\to\varOmega^2S^{2n}$, $G_{k}^{n}$ approximates $\varOmega^2S^{2n}$.
AMS 2000 Mathematics subject classification: Primary 55P35