Algebraic topology of Peano continua

Katsuya Eda

doi:10.1016/j.topol.2003.11.012

Algebraic topology of Peano continua

Katsuya Eda

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

7 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	213-226
Number of pages	14
Journal	Topology and its Applications
Volume	153
Issue number	2-3 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.topol.2003.11.012
Publication status	Published - 2005 Sep 1

Keywords

Fundamental group
Homology group
Peano continua

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2003.11.012

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title = "Algebraic topology of Peano continua",

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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doi = "10.1016/j.topol.2003.11.012",

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T1 - Algebraic topology of Peano continua

AU - Eda, Katsuya

PY - 2005/9/1

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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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