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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
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