Power Maps on Quasi-$p$-regular SU(n)

Abstract

In the paper we will introduce 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, James and Barrett.