### Abstract

Let X be a Peano continuum. Then the following hold: (1) The singular cohomology group H^{1}(X) is isomorphic to the Čech cohomology group Ȟ^{1}(X). (2) For each homomorphism h: π_{1}(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: π_{1}(X) → G_{0} * G_{1} there exists a finitely generated subgroup F_{0} of G_{0} or a finitely generated subgroup F_{1} of G_{1} such that Im(h) ⊆ F_{0} * G_{1} or Im(h) ⊆ G_{0} * F_{1}.

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 | |

Publication status | Published - 2005 Sep 1 |

### Fingerprint

### Keywords

- Fundamental group
- Homology group
- Peano continua

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Topology and its Applications*,

*153*(2-3 SPEC. ISS.), 213-226. https://doi.org/10.1016/j.topol.2003.11.012

**Algebraic topology of Peano continua.** / Eda, Katsuya.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 153, no. 2-3 SPEC. ISS., pp. 213-226. https://doi.org/10.1016/j.topol.2003.11.012

}

TY - JOUR

T1 - Algebraic topology of Peano continua

AU - Eda, Katsuya

PY - 2005/9/1

Y1 - 2005/9/1

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

UR - http://www.scopus.com/inward/record.url?scp=27644528571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644528571&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2003.11.012

DO - 10.1016/j.topol.2003.11.012

M3 - Article

AN - SCOPUS:27644528571

VL - 153

SP - 213

EP - 226

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 2-3 SPEC. ISS.

ER -