The homology of double loop spaces of complex Stiefel manifolds (Q1090972)

The author computes the mod-p homology, \(p\geq 2\), for the double loop space of SU(n)/SU(k). He also gives the action of the Steenrod algebra together with the Bockstein spectral sequence. Finally, he gives the algebra structure for the mod-p homology of the triple loop space for \((SU(n)/SU(k))<3>\). The answers obtained agree with those in the unpublished thesis of \textit{D. Waggoner} [Univ. Kentucky, August, 1985]. In addition, Waggoner gives the action of the Dyer-Lashof operations on the 4-fold loop space \(\Omega^ 3(SU(n)<3>)\), the coproduct in the homology of some of the spaces \(\Omega^ 3(SU(n)/SU(k))<3>\), and an allied product decomposition for the space of pointed maps \(map_*(RP^ 2,\Omega SU(4))\) in terms of the fibre of the double suspension.