Algebraic topology of Peano continua

Katsuya Eda

doi:10.1016/j.topol.2003.11.012

Algebraic topology of Peano continua

Katsuya Eda^*

^*この研究の対応する著者

研究成果: Article › 査読

7 被引用数 (Scopus)

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Let X be a Peano continuum. Then the following hold: (1) The singular cohomology group H¹(X) is isomorphic to the Čech cohomology group Ȟ¹(X). (2) For each homomorphism h: π₁(X) → *_i∈I G_i there exists a finite subset F of I such that Im(h) ⊆ *_i∈F G_i. (3) For each injective homomorphism h: π₁(X) → G₀ * G₁ there exists a finitely generated subgroup F₀ of G₀ or a finitely generated subgroup F₁ of G₁ such that Im(h) ⊆ F₀ * G₁ or Im(h) ⊆ G₀ * F₁.

本文言語	English
ページ（範囲）	213-226
ページ数	14
ジャーナル	Topology and its Applications
巻	153
号	2-3 SPEC. ISS.
DOI	https://doi.org/10.1016/j.topol.2003.11.012
出版ステータス	Published - 2005 9月 1

ASJC Scopus subject areas

幾何学とトポロジー

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10.1016/j.topol.2003.11.012

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abstract = "Let X be a Peano continuum. Then the following hold: (1) The singular cohomology group H1(X) is isomorphic to the {\v C}ech cohomology group Ȟ1(X). (2) For each homomorphism h: π1(X) → *i∈I Gi there exists a finite subset F of I such that Im(h) ⊆ *i∈F Gi. (3) For each injective homomorphism h: π1(X) → G0 * G1 there exists a finitely generated subgroup F0 of G0 or a finitely generated subgroup F1 of G1 such that Im(h) ⊆ F0 * G1 or Im(h) ⊆ G0 * F1.",

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N2 - Let X be a Peano continuum. Then the following hold: (1) The singular cohomology group H1(X) is isomorphic to the Čech cohomology group Ȟ1(X). (2) For each homomorphism h: π1(X) → *i∈I Gi there exists a finite subset F of I such that Im(h) ⊆ *i∈F Gi. (3) For each injective homomorphism h: π1(X) → G0 * G1 there exists a finitely generated subgroup F0 of G0 or a finitely generated subgroup F1 of G1 such that Im(h) ⊆ F0 * G1 or Im(h) ⊆ G0 * F1.

AB - Let X be a Peano continuum. Then the following hold: (1) The singular cohomology group H1(X) is isomorphic to the Čech cohomology group Ȟ1(X). (2) For each homomorphism h: π1(X) → *i∈I Gi there exists a finite subset F of I such that Im(h) ⊆ *i∈F Gi. (3) For each injective homomorphism h: π1(X) → G0 * G1 there exists a finitely generated subgroup F0 of G0 or a finitely generated subgroup F1 of G1 such that Im(h) ⊆ F0 * G1 or Im(h) ⊆ G0 * F1.

KW - Fundamental group

KW - Homology group

KW - Peano continua

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Algebraic topology of Peano continua

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