部分射影四元数Stiefel流形的上同调环

Pub Date : 2022-01-01 DOI:10.1070/SM9601
G. E. Zhubanov, F. Y. Popelenskii
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引用次数: 0

摘要

四元数Stiefel流形是纤维束在相应的格拉斯曼流形上的总空间。这个群在这个束的纤维上自由活动。商空间称为四元数投影Stiefel流形。它的真实和复杂的类似物早前被一些作者积极地研究过。自由作用于三维球面上的有限群也自由而离散地作用于四元数Stiefel束的纤维上。相应的商空间称为部分射影Stiefel流形。计算了系数为的部分投影四元数Stiefel流形的上同调环,其中为素数。参考书目:14篇。
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On the cohomology rings of partially projective quaternionic Stiefel manifolds
The quaternionic Stiefel manifold is the total space of a fibre bundle over the corresponding Grassmannian . The group 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 , where is prime, are calculated. Bibliography: 14 titles.
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