Generating varieties for the triple loop space of classical Lie groups
Volume 177 / 2003
Fundamenta Mathematicae 177 (2003), 269-283
MSC: Primary 58D27; Secondary 53C07, 55R40.
DOI: 10.4064/fm177-3-6
Abstract
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.
