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Iriye, Kouyemon; Kono, Akira

Mod \(p\) retracts of \(G\)-product spaces. (English) Zbl 0554.55004

Math. Z. 190, 357-363 (1985).
Let \(G\) be a transitive permutation group of degree \(n\), \(n>1\), and \(X\) be a space. By an embedding \(X=X\times *\times\cdots\times *\subset (X)^n\to (X)^n/G\) we regard \(X\) as a subspace of \((X)^n/G\). In this paper we answer the following question: Let \(X\) be a nilpotent space and \(p\) be a prime or 0. When is \(X_{(p)}\) a retract of \((X_{(p)})^n/G ?\) One of the main tools is a geometrical transfer map.
Reviewer: Kouyemon Iriye

Cited in 8 Documents

MSC:

55P60 Localization and completion in homotopy theory
55P91 Equivariant homotopy theory in algebraic topology
54C15 Retraction

Keywords:

nilpotent space; geometrical transfer map; localized symmetric product space; mod p retract
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References:

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