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 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.
Original language | English |
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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 |
Keywords
- Fundamental group
- Homology group
- Peano continua
ASJC Scopus subject areas
- Geometry and Topology