Homotopy Theory of Classifying Spaces of Compact Lie Groups

1994 ◽  
pp. 81-123 ◽  
Author(s):  
Stefan Jackowski ◽  
James McClure ◽  
Bob Oliver
Keyword(s):  
Lie Groups ◽  
Homotopy Theory ◽  
Classifying Spaces ◽  
Compact Lie Groups

A Remark on Maps Between Classifying Spaces of Compact Lie Groups

1988 ◽  
Vol 31 (4) ◽  
pp. 452-458 ◽  
Author(s):  
Zdzisław Wojtkowiak
Keyword(s):  
Weyl Group ◽  
Lie Groups ◽  
Finite Groups ◽  
Classifying Spaces ◽  
Compact Lie Groups ◽  
Rational Cohomology

AbstractWe 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 4- Z/3) into BSO(3) which is not induced by a homomorphism.

Maps between p-completed classifying spaces

1989 ◽  
Vol 112 (3-4) ◽  
pp. 231-235 ◽  
Author(s):  
J. Frank Adams ◽  
Zdzisław Wojtkowiak
Keyword(s):  
Lie Groups ◽  
Classifying Spaces ◽  
Compact Lie Groups ◽  
Complete Case ◽  
Topological Map ◽  
Maximal Tori ◽  
Local Case ◽  
Admissible Maps

SynopsisLet G and G' be two connected compact Lie groups with maximal tori T and T'. For a space X, let Xp be the p-completion of X. We will associate to each topological map f:(BG)p→(BG')p an “admissible map” ϕ:π1(T)⊗zZp→π1(T′)⊗zZp. We then show that the study of “admissible maps” in the p-complete case may be reduced to their study in the p-local case.

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