Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Power maps on quasi-$p$-regular $SU(n)$

Pages: 235 – 254

DOI: http://dx.doi.org/10.4310/HHA.2015.v17.n1.a11


Andrew Russhard (Mathematical Sciences, University of Southampton, Highfield, Southampton, United Kingdom)


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.

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Published 18 May 2015