Abstract
Fix an m ∈ ℕ, m ≥ 2. Let Y be a simply connected pointed CW-complex, and let B be a finite set of continuous mappings a: Sm → Y respecting the distinguished points. Let Γ(a) ⊂ Sm × Y be the graph of a, and we denote by [a] ∈ πm(Y) the homotopy class of a. Then for some r ∈ ℕ depending on m only, there exist a finite set E ⊂ Sm × Y and a mapping k: E(r) = {F ⊂ E: |F| ≤ r} → πm(Y) such that for each a ∈ B we have
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 159–194.
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Podkorytov, S.S. Mappings of the sphere to a simply connected space. J Math Sci 140, 589–610 (2007). https://doi.org/10.1007/s10958-007-0441-6
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DOI: https://doi.org/10.1007/s10958-007-0441-6