Geodesic
Functor $D$ and strong homotopy
Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 557-564.

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This paper studies functor $D$ and strong homotopy, introduced earlier by the author [1]. A theorem is proven on mappings, and the connection is established between the concepts of strong homotopy of DGA-mapping of coalgebras and functor $D$. As topological applications, in particular, it is shown that continuous mappings of the sphere $f,g:S^{2n-1}\to S^n$ have one and the same Hopf invariant if and only if the induced chain of mappings is strongly homotopic. 
@article{MZM_1977_21_4_a13,
     author = {V. A. Smirnov},
     title = {Functor $D$ and strong homotopy},
     journal = {Matemati\v{c}eskie zametki},
     pages = {557--564},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a13/}
}
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V. A. Smirnov. Functor $D$ and strong homotopy. Matematičeskie zametki, Tome 21 (1977) no. 4, pp. 557-564. http://geodesic.mathdoc.fr/item/MZM_1977_21_4_a13/