Homology, Homotopy and Applications
Volume 17 (2015)
Power maps on quasi-$p$-regular $SU(n)$
Pages: 235 – 254
In the paper we will show that the $p^3$ power map on $SU(p+t-1)$ is an H-map for $2 \leq t \leq p-1$. To do this we will consider a fibration whose base space is $SU(p+t-1)$ with the property that there is a section into the total space. We will then use decomposition methods to identify the fibre and the map from it to the total space. This information will be used to deduce information about $SU(p+t-1)$. In doing this we draw together recent work of Kishimoto and Theriault with more classical work of Cohen and Neisendorfer, and make use of the classical theorems of Hilton and Milnor, and James and Barrett.
power map, Lie group, quasi-$p$-regular
2010 Mathematics Subject Classification
Primary 55P35. Secondary 55T99.