A POLYNOMIAL MODEL FOR THE DOUBLE-LOOP SPACE OF AN EVEN SPHERE

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...

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Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 47; no. 1; pp. 155 - 162
Main Author Kamiyama, Yasuhiko
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2004
Cambridge University Press (CUP)
Subjects
even sphere
loop space
rational function
rational function
loop space
even sphere
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ISSN0013-0915
1464-3839
1464-3839
DOI10.1017/S001309150300052X

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Summary: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
Bibliography:ark:/67375/6GQ-T2VSZS50-M
PII:S001309150300052X
ArticleID:00052
istex:9CB43B2E7559B5D467C271E34BA7C21E929C32DE
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0013-0915
1464-3839
1464-3839
DOI:10.1017/S001309150300052X