TORAL GROUPS AND CLASSIFYING SPACES OF p–COMPACT GROUPS by
نویسنده
چکیده
It is knwon [23] that if p is odd, NpT is isomorphic to the semidirect product T oWp, and the fibration (BT )p (BNpT )p BWp has a section. The classifying spaces of NpT and other p–toral subgroups of K have been extensively used for the study of BK at the prime p, [13] etc. We note, however, that for the normalizer NT the loop space of (BNT )p need not be a p–compact toral group. In fact, if p does not divide the order of the Weyl group, then (BNT )p ' (BK)p . We will discuss more about (BNT )p later.
منابع مشابه
Homotopy Theory of Lie groups and their Classifying Spaces
1. Lie groups, homomorphisms and linear representations. Irreducible representations. 2. Maximal tori in compact Lie groups. 3. Characters of representations. Ring of virtual characters. The Weyl theorem. 4. Actions of Lie groups. Homogeneous spaces (orbits) and equivariant maps. 5. Classifying spaces of topological groups and maps induced by homomorphisms. 6. Homotopy classification of maps be...
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