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- Title
On the higher order exterior and interior Whitehead products.
- Authors
Golasiński, Marek; Melo, Thiago
- Abstract
We extend the notion of the exterior Whitehead product for maps $$\alpha _i{:}\,\Sigma A_i \rightarrow X_i$$ for $$i=1,\ldots ,n$$ , where $$\Sigma A_i$$ is the reduced suspension of $$A_i$$ and then, for the interior product with $$X_i=J_{m_i}(X)$$ , the $$m_i$$ th-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 $$\circ $$ (called the Theriault product) to a sequence $$X_1,\ldots ,X_n$$ of simply connected co- H-spaces to obtain a higher Gray-Whitehead product map where $$T_1(X_1,\ldots ,X_n)$$ is the fat wedge of $$X_1,\ldots ,X_n$$ .
- Publication
Manuscripta Mathematica, 2017, Vol 152, Issue 1/2, p167
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/s00229-016-0857-8