# Homotopy and homology groups of the n-dimensional Hawaiian earring

Katsuya Eda; Kazuhiro Kawamura

Fundamenta Mathematicae (2000)

- Volume: 165, Issue: 1, page 17-28
- ISSN: 0016-2736

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topEda, Katsuya, and Kawamura, Kazuhiro. "Homotopy and homology groups of the n-dimensional Hawaiian earring." Fundamenta Mathematicae 165.1 (2000): 17-28. <http://eudml.org/doc/212457>.

@article{Eda2000,

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.},

author = {Eda, Katsuya, Kawamura, Kazuhiro},

journal = {Fundamenta Mathematicae},

keywords = {homology group; Čech homotopy group; n-dimensional Hawaiian earring},

language = {eng},

number = {1},

pages = {17-28},

title = {Homotopy and homology groups of the n-dimensional Hawaiian earring},

url = {http://eudml.org/doc/212457},

volume = {165},

year = {2000},

}

TY - JOUR

AU - Eda, Katsuya

AU - Kawamura, Kazuhiro

TI - Homotopy and homology groups of the n-dimensional Hawaiian earring

JO - Fundamenta Mathematicae

PY - 2000

VL - 165

IS - 1

SP - 17

EP - 28

AB - 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.

LA - eng

KW - homology group; Čech homotopy group; n-dimensional Hawaiian earring

UR - http://eudml.org/doc/212457

ER -

## References

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- [6] K. Eda and K. Kawamura, The singular homology of the Hawaiian earring, J. London Math. Soc., to appear. Zbl0958.55004
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