Abstract
We introduce a notion of rank completion for bi-modules over a finite tracial von Neumann algebra. We show that the functor of rank completion is exact and that the category of complete modules is abelian with enough projective objects. This leads to interesting computations in the L 2-homology for tracial algebras. As an application, we also give a new proof of a Theorem of Gaboriau on invariance of L 2-Betti numbers under orbit equivalence.
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Thom, A. (2008). L 2-invariants and Rank Metric. In: Burghelea, D., Melrose, R., Mishchenko, A.S., Troitsky, E.V. (eds) C*-algebras and Elliptic Theory II. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8604-7_14
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DOI: https://doi.org/10.1007/978-3-7643-8604-7_14
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