On the higher order exterior and interior Whitehead products
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Data
2017-01-01
Autores
Golasiński, Marek
de Melo, Thiago [UNESP]
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Resumo
We extend the notion of the exterior Whitehead product for maps αi:ΣAi→Xi for i= 1, …, n, where Σ Ai is the reduced suspension of Ai and then, for the interior product with Xi=Jmi(X), the mith-stage of the James construction J(X) as well. The main result stated in Theorem 4.10 generalizes (Hardie in Q J Math Oxford Ser 12(2):196–204, 1961, Theorem 1.10) and concerns to the Hopf invariant of the generalized Hopf construction. We close the paper applying Gray’s construction ∘ (called the Theriault product) to a sequence X1, …, Xn of simply connected co-H-spaces to obtain a higher Gray–Whitehead product map (Formula presented.), where T1(X1, …, Xn) is the fat wedge of X1, …, Xn.
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55S15, Primary 55Q15, Secondary 55Q25
Como citar
Manuscripta Mathematica, v. 152, n. 1-2, p. 167-188, 2017.