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COHOMOLOGICAL DIMENSION OF MACKEY FUNCTORS FOR INFINITE GROUPS
Published online by Cambridge University Press: 25 October 2006
Abstract
We consider the cohomology of Mackey functors for infinite groups and define the Mackey-cohomological dimension ${\rm cd}_{{\mathfrak M}} G$ of a group $G$. We will relate this dimension to other cohomological dimensions such as the Bredon-cohomological dimension ${\rm cd}_{{\mathfrak F}}G$ and the relative cohomological dimension ${{\mathfrak F}}\text{-}{\rm cd} G$. In particular, we show that for virtually torsion free groups the Mackey-cohomological dimension is equal to both ${{\mathfrak F}}\text{-}{\rm cd} G$ and the virtual cohomological dimension.
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- The London Mathematical Society 2006
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