Cohomological Dimension With Respect to Nonabelian Groups

This dissertation addresses three aspects of cohomological dimension of metric spaces with respect to nonabelian groups.

In the first part we examine when the Eilenberg-Maclane space (n = 1) of the abelianization of a solvable group being an absolute extensor of a metric space implies the Eilenberg-Maclane space of the group itself is an absolute extensor. We also give an elementary approach to this problem in the case of nilpotent groups and 2-dimensional metric spaces.

The next part of the dissertation is devoted to generalizations of the Cencelj- Dranishnikov theorems relating extension properties of nilpotent CW complexes to its homology groups.

In the final part we extend the definition of Bockstein basis of abelian groups to nilpotent groups G, and prove a version of the First Bockstein Theorem for such groups.