The index of coset spaces of compact Lie groups
نویسندگان
چکیده
منابع مشابه
On Compact Complex Coset Spaces of Reductive Lie Groups
1. The statement of theorems. Let G be a connected complex Lie group and let B be a closed complex Lie subgroup in G. The left coset space G/B is a complex manifold, which will be called a complex coset space. We denote by Bo the identity connected component of B and U the normalizer of BoThe canonical projection p of G/B onto G/ U defines a holomorphic fibre bundle, and the complex Lie group U...
متن کاملLifts of Diffeomorphisms for Orbit Spaces of Compact Lie Groups
A structure of the group of diffeomorphisms for the orbit space of an orthogonal representation G → O(V ) of a compact Lie group G is studied. For a finite G it is proved that each diffeomorphism of the orbit space V/G has a smooth lift and the group of components of the group of Diff(V/G) is described, especially in the case when G is a finite Coxeter group. Similar results are obtained for th...
متن کاملSelf-maps of Classifying Spaces of Compact Simple Lie Groups
We describe here the set [BG, BG] of homotopy classes of self-maps of the classifying space BG , for any compact connected simple Lie group G. In particular, we show that two maps ƒ , f : BG —• BG are homotopic if and only if they are homotopic after restricting to the maximal torus of G ; or equivalently if and only if they induce the same homomorphism in rational cohomology. In addition, we i...
متن کاملHomotopy Theory of Classifying Spaces of Compact Lie Groups
The basic problem of homotopy theory is to classify spaces and maps between spaces, up to homotopy, by means of invariants like cohomology. In the last decade some striking progress has been made with this problem when the spaces involved are classifying spaces of compact Lie groups. For example, it has been shown, for G connected and simple, that if two self maps of BG agree in rational cohomo...
متن کاملVector Bundles over Classifying Spaces of Compact Lie Groups
The completion theorem of Atiyah and Segal [AS] says that the complex K-theory group K(BG) of the classifying space of any compact Lie group G is isomorphic to R(G)̂ : the representation ring completed with respect to its augmentation ideal. However, the group K(BG) = [BG,Z × BU ] does not directly contain information about vector bundles over the infinite dimensional complex BG itself. The purp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1962
ISSN: 0025-5645
DOI: 10.2969/jmsj/01410026