Homology, Homotopy and Applications

Volume 11 (2009)

Number 1

Homotopy nilpotency in localized $SU(n)$

Pages: 61 – 79

DOI: https://dx.doi.org/10.4310/HHA.2009.v11.n1.a4


Daisuke Kishimoto (Department of Mathematics, Kyoto University, Kyoto, Japan)


We determine the homotopy nilpotency of $p$-localized $SU(n)$ when $p$ is a quasi-regular prime in the sense of M. Mimura and H. Toda, “Cohomology operations and homotopy of compact Lie groups I,” Topology 9 (1970), 317-336. As a consequence, we see that it is not a monotonic decreasing function in $p$.


homotopy nilpotency, localization

2010 Mathematics Subject Classification

55P60, 55Q15

Published 1 January 2009