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Torsion invariants for finite von Neumann algebras. (English) Zbl 0827.47015
Curto, Raúl E. (ed.) et al., Multivariable operator theory. A joint summer research conference on multivariable operator theory, July 10-18, 1993, University of Washington, Seattle, WA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 185, 151-186 (1995).
Summary: We define a numerical torsion invariant for an $$n$$-tuple $$T$$ of commuting elements in a finite von Neumann algebra $${\mathcal A}$$ and study properties of this torsion. New spectral invariants supported on the spectrum $$\sigma (T)$$ are also discussed and are related to the torsion invariant as well as certain invariants of Novikov-Shubin. We use the torsion invariant to get a homotopy invariant for a compact oriented Riemannian manifold and a torsion-index for a family of elliptic operators.
For the entire collection see [Zbl 0819.00022].

##### MSC:
 47B20 Subnormal operators, hyponormal operators, etc. 47A67 Representation theory of linear operators 46L45 Decomposition theory for $$C^*$$-algebras