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COHOMOLOGICAL DIMENSION OF MACKEY FUNCTORS FOR INFINITE GROUPS

Published online by Cambridge University Press:  25 October 2006

CONCHITA MARTINEZ-PÉREZ
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, Zaragoza 50009, [email protected]
BRITA E. A. NUCINKIS
Affiliation:
School of Mathematics, University of Southampton, Southampton SO17 1BJ, United [email protected]
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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.

Type
Notes and Papers
Copyright
The London Mathematical Society 2006

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