Homotopy and homology groups of the n-dimensional Hawaiian earring

Volume 165 / 2000

Katsuya Eda, Kazuhiro Kawamura Fundamenta Mathematicae 165 (2000), 17-28 DOI: 10.4064/fm-165-1-17-28

Abstract

For the n-dimensional Hawaiian earring $ℍ_n,$ n ≥ 2, $π _n(ℍ_n,o)≃ ℤ^ω$ and $π_i(ℍ_n, o)$ is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CX ∨ CY be the one-point union with two points of the base spaces X and Y being identified to a point. Then $H_n(X∨Y) ≃ H_{n}(X) ⊕ H_n(Y) ⊕ H_{n}(CX∨CY)$ for n ≥ 1.

Authors

  • Katsuya Eda
  • Kazuhiro Kawamura

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