Geodesic
Generating varieties for the triple loop space of classical Lie groups
Yasuhiko Kamiyama1
1 Department of Mathematics University of the Ryukyus Okinawa 903-0213, Japan
Fundamenta Mathematicae, Tome 177 (2003) no. 3, pp. 269-283

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

For $G= SU(n), Sp(n)$ or $\mathop {\rm Spin}\nolimits (n)$, let $C_G (SU(2))$ be the centralizer of a certain $SU(2)$ in $G$. We have a natural map $J: G/C_G (SU(2)) \rightarrow {\mit \Omega }_0^3 G$. For a generator $\alpha $ of $H_\ast (G/C_G (SU(2)); {{\mathbb Z}}/2)$, we describe $J_\ast (\alpha )$. In particular, it is proved that $J_\ast : H_\ast (G/C_G (SU(2)); {{\mathbb Z}}/2) \rightarrow H_\ast ({\mit \Omega }_0^3G;{{\mathbb Z}}/2)$ is injective.
DOI : 10.4064/fm177-3-6
Keywords: mathop spin nolimits centralizer certain have natural map rightarrow mit omega generator alpha ast mathbb describe ast alpha particular proved ast ast mathbb rightarrow ast mit omega mathbb injective

Yasuhiko Kamiyama 1

1 Department of Mathematics University of the Ryukyus Okinawa 903-0213, Japan 
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Yasuhiko Kamiyama. Generating varieties for the triple loop space
 of classical Lie groups. Fundamenta Mathematicae, Tome 177 (2003) no. 3, pp. 269-283. doi: 10.4064/fm177-3-6

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