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

Eda Katsuya, Kazuhiro Kawamura

Research output: Contribution to journalArticle

17 Citations (Scopus)

### Abstract

For the n-dimensional Hawaiian earring ℍn, n ≥ 2, πn(ℍn, o) ≃ ℤω and πi(ℍn,o) is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CXVCY be the one-point union with two points of the base spaces X and Y being identified to a point. Then Hn(X V Y) ≃ Hn(X) ⊕ Hn(Y) ⊕ Hn(CX V CY) for n ≥ 1.

Original language English 17-28 12 Fundamenta Mathematicae 165 1 Published - 2000

### Fingerprint

Homotopy Groups
Homology Groups
n-dimensional
Trivial
Union
Cone

### Keywords

• Cech homotopy group
• Homology group
• n-dimensional Hawaiian earring

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

Homotopy and homology groups of the n-dimensional Hawaiian earring. / Katsuya, Eda; Kawamura, Kazuhiro.

In: Fundamenta Mathematicae, Vol. 165, No. 1, 2000, p. 17-28.

Research output: Contribution to journalArticle

Katsuya, E & Kawamura, K 2000, 'Homotopy and homology groups of the n-dimensional Hawaiian earring', Fundamenta Mathematicae, vol. 165, no. 1, pp. 17-28.
Katsuya, Eda ; Kawamura, Kazuhiro. / Homotopy and homology groups of the n-dimensional Hawaiian earring. In: Fundamenta Mathematicae. 2000 ; Vol. 165, No. 1. pp. 17-28.
title = "Homotopy and homology groups of the n-dimensional Hawaiian earring",
abstract = "For the n-dimensional Hawaiian earring ℍn, n ≥ 2, πn(ℍn, o) ≃ ℤω and πi(ℍn,o) is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CXVCY be the one-point union with two points of the base spaces X and Y being identified to a point. Then Hn(X V Y) ≃ Hn(X) ⊕ Hn(Y) ⊕ Hn(CX V CY) for n ≥ 1.",
keywords = "Cech homotopy group, Homology group, n-dimensional Hawaiian earring",
author = "Eda Katsuya and Kazuhiro Kawamura",
year = "2000",
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AB - For the n-dimensional Hawaiian earring ℍn, n ≥ 2, πn(ℍn, o) ≃ ℤω and πi(ℍn,o) is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CXVCY be the one-point union with two points of the base spaces X and Y being identified to a point. Then Hn(X V Y) ≃ Hn(X) ⊕ Hn(Y) ⊕ Hn(CX V CY) for n ≥ 1.

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KW - Homology group

KW - n-dimensional Hawaiian earring

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