复Stiefel流形的商空间

THE QUOTIENT SPACES OF COMPLEX STIEFEL MANIFOLDS

本文研究了复Stiefel流形关于群S1的商空间的伦型,并且计算了该空间的上同调群.通过纤维化,为这些商空间的上同调找到一组典则的生成元.再利用推广的吴公式,讨论了这些生成元在Sqi下的行为.最后,作为应用,本文对S.Gitler和D.Handel的结果作了部分改进.

The thesis is devotes to studying the homotopy of the quotient of complex Stiefel manifolds by the groups S1 and calculating the mod 2 cohomology of the quotients. By fibrations, the author finds a series of canonical generators for the cohomology of these spaces. Making use of general Wu formulae, the actions of Sqi on the generators are discussed. Finally, as an application, the author improves the work that S.Gilter and D. Handel did.