The von Neumann Dimension
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Betti numbers are dimensions of (co)homology groups. In the presence of a group action, we can alternatively also use an equivariant version of dimension; this leads to L2-Betti numbers. In this chapter, we will introduce such an equivariant version of dimension, using the group von Neumann algebra. In Chap. 3, this dimension will allow us to define L2-Betti numbers of groups and spaces.
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