TheZ *-theorem for compact Lie groups

Mislin, Guido; Thévenaz, Jacques

doi:10.1007/bf01445193

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Normal ^-Subgroups Of Connected Lie Groups1

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1994

1996

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Cited by 4 publications

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“…Let Cg(Z(n)) denote the centralizer of Z(n) in G. Then BCG(Z(n))$ ~ map(BZ(n),BG$)Bi by [7]. Since the map BCG(Z(n))$ -» BGp is a homotopy equivalence and 7To(C7) is a p-group, a result of Mislin and Thévenaz [15] shows Z(n) is central in G. Thus we obtain the homotopy commutative diagrams of fibrations associated with Z(n) -y G -» G/Z(n) :…”

Section: Normal ^-Subgroups Of Connected Lie Groupsmentioning

confidence: 97%

Fibrations of Classifying Spaces

Ishiguro¹,

Notbohm²

1994

Transactions of the American Mathematical Society

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Abstract. We investigate fibrations of the form Z -» Y -► X, where two of the three spaces are classifying spaces of compact connected Lie groups. We obtain certain finiteness conditions on the third space which make it also a classifying space. Our results allow to express some of the basic notions in group theory in terms of homotopy theory, i.e., in terms of classifying spaces. As an application we prove that every retract of the classifying space of a compact connected Lie group is again a classifying space.

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Section: Normal ^-Subgroups Of Connected Lie Groupsmentioning

confidence: 97%