Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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SELF-MAPS ON M(ℤq, n + 2) ∨ M(ℤq, n + 1) ∨ M(ℤq, n)

  • Ho Won Choi (Faculty of Liberal Arts and Teaching Kangnam University)
  • Received : 2023.08.17
  • Accepted : 2023.11.14
  • Published : 2023.11.30
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Abstract

When G is an abelian group, we use the notation M(G, n) to denote the Moore space. The space X is the wedge product space of Moore spaces, given by X = M(ℤq, n+ 2) ∨ M(ℤq, n+ 1) ∨ M(ℤq, n). We determine the self-homotopy classes group [X, X] and the self-homotopy equivalence group 𝓔(X). We investigate the subgroups of [Mj , Mk] consisting of homotopy classes of maps that induce the trivial homomorphism up to (n + 2)-homotopy groups for j ≠ k. Using these results, we calculate the subgroup 𝓔dim#(X) of 𝓔(X) in which all elements induce the identity homomorphism up to (n + 2)-homotopy groups of X.

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References

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