A remark on maps between classifying spaces of compact Lie groups.

Zdzislaw, Jozef Wojtkowiak (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

We show that two maps between classifying spaces of compact, connected Lie groups are homotopic after inverting the order of the Weyl group of the source if and only if they induce the same maps on rational cohomology. We shall also give some results on maps from classifying spaces of finite groups to classifying spaces of compact Lie groups. Among other things we construct a map from B(Z/2+Z/2+Z/3) into BSO(3) which is not induced by a homomorphism.

Domains: Mathematics [math]; Algebraic Topology [math.AT]

Zdzislaw, Jozef Wojtkowiak. A remark on maps between classifying spaces of compact Lie groups. . Canadian Mathematical Bulletin, 1988, 31 (4). ⟨hal-01293284⟩