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Reducing equivariant homotopy theory to the theory of fibrations. (English) Zbl 0571.55010
Algebraic topology, Proc. Conf. in Honor of P. Hilton, St. John’s/Can. 1983, Contemp. Math. 37, 35-49 (1985).
[For the entire collection see Zbl 0549.00016.]
Let G be a topological group and \(\{G_ a\}_{a\in A}^ a \)set of subgroups of G. The corresponding equivariant homotopy theory is a well- known concept [G. E. Bredon, Equivariant cohomology theories, Lect. Notes Math. 34 \((1967+\) Zbl 0162.272)]. This paper shows that in the commonly occurring case if the subgroups \(G_ a\) of G, \(a\in A\), are rigid (e.g. normal), then this equivariant homotopy theory is equivalent to a homotopy theory of fibrations, indexed by a partial order. The proof uses freely notation and terminology from six other papers of the authors.