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.

Résumé

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.

Détail

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