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On Pierce-like idempotents and Hopf invariants. (English) Zbl 1036.55003
In the pointed homotopy category, let $$A$$ be a commutative cogroup and $$Y=Y_1\vee\cdots \vee Y_n$$ where $$n\geq 2$$. The authors define and study a complete set of idempotents on $$[A,Y]$$. They show that a map $$f: X\rightarrow Y$$ induces a generalized Hopf invariant HI$$_f$$ which is a functorial sum of HI$$_L$$ for $$L\subset \{1,\dots,n\}$$, $$| L| \geq 2$$. This work is related to P. Selick [Topology 17, 407–412 (1978; Zbl 0403.55021)], M.Walker [J. Lond. Math. Soc., II Ser.19, 153–155 (1979; Zbl 0407.55015)] and P. Hilton [Fundam. Math. 61, 199–214 (1967; Zbl 0171.44202)].

##### MSC:
 55Q25 Hopf invariants 55P30 Eckmann-Hilton duality 55P45 $$H$$-spaces and duals
##### Keywords:
wedge decomposition; idempotents; Hopf invariants
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