Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HOMOTOPY PROPERTIES OF map(ΣnℂP2, Sm)

  • Received : 2020.05.07
  • Accepted : 2020.10.16
  • Published : 2021.05.01
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Abstract

For given spaces X and Y, let map(X, Y) and map*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map*(X, Y ; g) be the path component of map(X, Y) containing f and map*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane πn+m(ΣnℂP2) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣnℂP2, Sm) up to homotopy equivalence. We also determine the generalized Gottlieb groups Gn(ℂP2, Sm). Finally, we compute homotopy groups of mapping spaces map(ΣnℂP2, Sm; f) for all generators [f] of [ΣnℂP2, Sm], and Gottlieb groups of mapping components containing constant map map(ΣnℂP2, Sm; *).

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References

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