Homotopy and homology groups of the n-dimensional Hawaiian earring

Eda Katsuya; Kazuhiro Kawamura

Homotopy and homology groups of the n-dimensional Hawaiian earring

Eda Katsuya^*, Kazuhiro Kawamura

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

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 CXVCY be the one-point union with two points of the base spaces X and Y being identified to a point. Then H_n(X V Y) ≃ H_n(X) ⊕ H_n(Y) ⊕ H_n(CX V CY) for n ≥ 1.

Original language	English
Pages (from-to)	17-28
Number of pages	12
Journal	Fundamenta Mathematicae
Volume	165
Issue number	1
Publication status	Published - 2000

Keywords

Cech homotopy group
Homology group
n-dimensional Hawaiian earring

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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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.",

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AU - Kawamura, Kazuhiro

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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.

KW - Cech homotopy group

KW - Homology group

KW - n-dimensional Hawaiian earring

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Homotopy and homology groups of the n-dimensional Hawaiian earring

Abstract

Keywords

ASJC Scopus subject areas

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