### Abstract

Let G be an Abelian group admitting a homomorphism α: ℤ→G such that the induced homomorphisms α⊗id: ℤ⊗G→G⊗G and α*: Hom(G,G)→Hom(ℤ,G) are isomorphisms. We show that for every simplicial complex L there exists an Edwards-Walsh resolution ω: EW_{G}(L,n)→ L . As applications of it we give several resolution theorems. In particular, we have Theorem. Let G be an arbitrary Abelian group. For every compactum X with c-dim_{G}X≤n there exists a G-acyclic map f: Z→X from a compactum Z with dimZ≤n+2 and c-dim_{G}Z≤n+1. Our methods determine other results as well. If the group G is cyclic, then one can obtain Z with dimZ≤n. In certain other cases, depending on G, we may resolve X in such a manner that dimZ≤n+1 and c-dim_{G}Z≤n.

Original language | English |
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Pages (from-to) | 175-204 |

Number of pages | 30 |

Journal | Topology and its Applications |

Volume | 120 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2002 May 15 |

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### Keywords

- Acyclic resolution
- Cohomological dimension
- Edwards-Walsh resolution

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Topology and its Applications*,

*120*(1-2), 175-204. https://doi.org/10.1016/S0166-8641(01)00015-3