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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

Yasuhiko Kamiyama
Affiliation:
Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-0213, Japan (kamiyama@sci.u-ryukyu.ac.jp)
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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
Copyright
Copyright © Edinburgh Mathematical Society 2004