\Z/p^\infty-acyclic resolutions of metrizable compacta
by
Leonard R. Rubin
University of Oklahoma
Coauthors: Philip J. Schapiro (Langston University)

We shall prove a G-acyclic resolution theorem for dim_G, cohomological dimension modulo the group G=\Z/p^\infty, in the class of metrizable compacta. This means that, given a metrizable compactum X such that dim_\Z/p^\infty X <= n (n >= 2), there exists a metrizable compactum Z and a surjective map \pi:Z\ra X such that:

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(a)" \pi is \Z/p^\infty-acyclic,

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(b)" dimZ <= n+1, and

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(c)" dim_\Z/p^\infty Z <= n. To say that a map \pi is G-acyclic, for an abelian group G, means that each fiber \pi^-1(x) of \pi is G-acyclic, i.e., that all the reduced Cech cohomology groups of \pi^-1(x) modulo the group G are trivial.

Date received: January 24, 2002