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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].

47B20 Subnormal operators, hyponormal operators, etc.
47A67 Representation theory of linear operators
46L45 Decomposition theory for \(C^*\)-algebras