Cohomological dimension and acyclic resolutions

Akira Koyama, Katsuya Yokoi

Research output: Contribution to journalArticle

8 Citations (Scopus)

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: EWG(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-dimGX≤n there exists a G-acyclic map f: Z→X from a compactum Z with dimZ≤n+2 and c-dimGZ≤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-dimGZ≤n.

Original languageEnglish
Pages (from-to)175-204
Number of pages30
JournalTopology and its Applications
Volume120
Issue number1-2
DOIs
Publication statusPublished - 2002 May 15
Externally publishedYes

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Compactum
Cohomological Dimension
Abelian group
Simplicial Complex
Homomorphisms
Theorem
Homomorphism
Resolve
Isomorphism
Arbitrary

Keywords

  • Acyclic resolution
  • Cohomological dimension
  • Edwards-Walsh resolution

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Cohomological dimension and acyclic resolutions. / Koyama, Akira; Yokoi, Katsuya.

In: Topology and its Applications, Vol. 120, No. 1-2, 15.05.2002, p. 175-204.

Research output: Contribution to journalArticle

Koyama, Akira ; Yokoi, Katsuya. / Cohomological dimension and acyclic resolutions. In: Topology and its Applications. 2002 ; Vol. 120, No. 1-2. pp. 175-204.
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