Journal of Mathematical Sciences

, Volume 140, Issue 4, pp 589–610 | Cite as

Mappings of the sphere to a simply connected space

  • S. S. Podkorytov


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
$$[a] = \sum\limits_{F \in E(r):F \subset \Gamma (a)} {k(F)} $$
. Bibliography: 5 titles.


Abelian Group Nonnegative Integer Commutative Diagram Spectral Sequence Simplicial Mapping 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • S. S. Podkorytov
    • 1
  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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