Abstract
In a recent series of papers (10), (11), (12), I. M. James has made an illuminating study of Stiefel manifolds. We shall begin by describing his results (for the complex case). Let Wn, k, for k > 1, denote the complex Stiefel manifold U(n)/U(n − k), where U(n) is the unitary group in n variables. Then we have a natural fibre map Wn, k → Wn, 1 = S2n−1, where Sr denotes the r-dimensional sphere. Let Pn, k, for k ≥ 1, denote the ‘stunted complex projective space’ obtained from the (n − 1)-dimensional complex projective space† Pn by identifying to a point a subspace Pn−k. Then we have a natural ‘cofibre map’ Pn, k → Pn, 1 = S2n−2. The space Pn, k is said to be S-reducible if some suspension of the map Pn, k → S2n−2 has a right homotopy inverse. The results of James can then be summarized as follows.
Publisher
Cambridge University Press (CUP)
Reference15 articles.
1. On the coefficient of a certain symmetric function;Mukohda;Jour. Fac. Sci. Niigata Univ.,1954
2. The Intrinsic Join: A Study of the Homotopy Groups of Stiefel Manifolds
3. Sur La Cohomologie des Espaces Fibres Principaux et des Espaces Homogenes de Groupes de Lie Compacts
4. On Chern characters and the structure of the unitary group;Adams;Proc. Comb. Phil. Soc.
Cited by
36 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献