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A POLYNOMIAL MODEL FOR THE DOUBLE-LOOP SPACE OF AN EVEN SPHERE
Published online by Cambridge University Press: 27 May 2004
Abstract
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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
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 1 , February 2004 , pp. 155 - 162
- Copyright
- Copyright © Edinburgh Mathematical Society 2004
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