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The von Neumann Dimension

  • Clara LöhEmail author
Chapter
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Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

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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Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany

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