Universal acyclic resolutions for arbitrary coefficient groups

Michael Levin

doi:10.4064/fm178-2-5

Universal acyclic resolutions for arbitrary coefficient groups

Michael Levin

Department of Mathematics

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

1 Scopus citations

Abstract

We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n + 1 and a surjective UV^n-1-map r : Z → X such that for every abelian group G and every integer k ≥ 2 such that dime X ≤ k ≤ n we have dime Z ≤ k and r is G-acyclic.

Original language	English
Pages (from-to)	159-169
Number of pages	11
Journal	Fundamenta Mathematicae
Volume	178
Issue number	2
DOIs	https://doi.org/10.4064/fm178-2-5
State	Published - 1 Jan 2003

Keywords

Cell-like and acyclic resolutions
Cohomological dimension

ASJC Scopus subject areas

Algebra and Number Theory

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10.4064/fm178-2-5

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abstract = "We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n + 1 and a surjective UVn-1-map r : Z → X such that for every abelian group G and every integer k ≥ 2 such that dime X ≤ k ≤ n we have dime Z ≤ k and r is G-acyclic.",

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author = "Michael Levin",

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N2 - We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n + 1 and a surjective UVn-1-map r : Z → X such that for every abelian group G and every integer k ≥ 2 such that dime X ≤ k ≤ n we have dime Z ≤ k and r is G-acyclic.

AB - We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n + 1 and a surjective UVn-1-map r : Z → X such that for every abelian group G and every integer k ≥ 2 such that dime X ≤ k ≤ n we have dime Z ≤ k and r is G-acyclic.

KW - Cell-like and acyclic resolutions

KW - Cohomological dimension

UR - https://www.scopus.com/pages/publications/0345357683

U2 - 10.4064/fm178-2-5

DO - 10.4064/fm178-2-5

M3 - Article

AN - SCOPUS:0345357683

SN - 0016-2736

VL - 178

SP - 159

EP - 169

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 2

ER -

Universal acyclic resolutions for arbitrary coefficient groups

Abstract

Keywords

ASJC Scopus subject areas

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