On the cohomology rings of partially projective quaternionic Stiefel manifolds

The quaternionic Stiefel manifold $V_{n,k}(\mathbb H)$ is the total space of a fibre bundle over the corresponding Grassmannian $G_{n,k}(\mathbb H)$. The group $\operatorname{Sp}(1)=S^3$ acts freely on the fibres of this bundle. The quotient space is called the quaternionic projective Stiefel manifold. Its real and complex analogues were actively studied earlier by a number of authors. A finite group acting freely on the three-dimensional sphere also acts freely and discretely on the fibres of the quaternionic Stiefel bundle. The corresponding quotient spaces are called partially projective Stiefel manifolds.The cohomology rings of partially projective quaternionic Stiefel manifolds with coefficients in $\mathbb Z_p$, where $p$ is prime, are calculated.Bibliography: 14 titles.

projective Stiefel manifold, discrete free group actions on