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Complexes that arise in cohomological dimension theory: A unified approach. (English) Zbl 0811.55001
In his celebrated proof of the equivalence of the cell-like mapping problem and the classical Aleksandrov problem about cohomological dimension of compacta, R. D. Edwards introduced a new, “combinatorial” approach to cohomological dimension (carefully and beautifully presented in details by the second author [Lect. Notes Math. 870, 105-118 (1981; Zbl 0474.55002)]), via, what is nowadays called the Edwards-Walsh complexes $$EW_ \mathbb{Z} (L,n)$$. This new framework was originally introduced only for $$G= \mathbb{Z}$$. Subsequently, A. N. Dranishnikov successfully adapted it for other groups $$G$$. The main purpose of the present paper is to present a unified exposition of the complexes $$EW_ G(L,n)$$, for arbitrary abelian groups $$G$$. As an application, an alternative construction is given (to that of A. N. Dranishnikov [Sib. Mat. J. 29, No. 1, 24-29 (1988); translation from Sib. Mat. Zh. 29, No. 1(167), 32-38 (1988; Zbl 0661.55002)]) of compacta realizing the classical Bockstein functions.

MSC:
 55M10 Dimension theory in algebraic topology
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