\(L^ 2\)-torsion invariants
The paper studies a generalization of Reidemeister-Franz torsion defined for smooth closed oriented manifolds which have the property that their \(L^ 2\)-cohomology vanishes and that their Novikov-Shubin invariants are positive. The invariant is a real number and constructed using the Fuglede-Kadison determinant instead of the ordinary determinant. The main results of the paper are that the invariant is a combinatorial invariant and satisfies a Künneth formula. Examples, where the invariant is non- trivial, are given. A more general construction of such an invariant taking values in algebraic \(K_ 1\)-groups of von Neumann algebras can be found in [the reviewer and \textit{M. Rothenberg}, \(K\)-theory 5, 213-264 (1991; Zbl 0748.57007)].
scientific article; zbMATH DE number 152030
scientific article