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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
Article

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

Keywords

Abelian Group Nonnegative Integer Commutative Diagram Spectral Sequence Simplicial Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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