Frank Neumann
A Theorem of Tits, Normalizers of Maximal Tori and Fibrewise Bousfield-Kan Completions
Preprint series: Mathematica Gottingensis

MSC:

20F55 Coxeter groups

20G20 Linear algebraic groups over the reals, the complexes, the quaternions

20J06 Cohomology of finite groups

22E15 General properties and structure of real Lie groups

57T15 Homology and cohomology of homogeneous spaces of Lie groups

Abstract: We use a theorem of Tits on the presentation of the normalizer
of a maximal torus of a connected compact semisimple Lie group
in terms of generators and relations to give several equivalent
conditions for the splitting of the associated normalizer
group extension and interprete them in terms of $p$-adic fibrewise
homotopy theory.
Keywords: compact Lie groups, Weyl group, fibrewise homotopy types