Suspension Splittings and Hopf Invariants for Retracts of the Loops on Co-h-spaces
نویسنده
چکیده
James constructed a functorial homotopy decomposition ΣΩΣX ' W∞ n=1 ΣX (n) for path-connected, pointed CW -complexes X. We generalize this to a functorial decomposition of ΣA where A is any functorial retract of a looped co-H space. This is used to construct Hopf invariants in a more general context. As well, when A = ΩY is the loops on a co-H space, we show that the wedge summands of ΣΩY further functorially decompose by using an action of an appropriate symmetric group.
منابع مشابه
Suspension Splittings and James-hopf Invariants for Retracts of the Loops on Co-h-spaces
James constructed a functorial homotopy decomposition ΣΩΣX ' ∨∞ n=1 ΣX (n) for path-connected, pointed CW -complexes X. We generalize this to a functorial decomposition of ΣA where A is any functorial retract of a looped co-H-space. This is used to construct Hopf invariants in a more general context. In addition, when A = ΩY is the loops on a co-H-space, we show that the wedge summands of ΣΩY f...
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