\(L^ 2\)-torsion invariants
type: Item
instance of: scholarly article
title: \(L^ 2\)-torsion invariants
zbMATH Open document ID: 0771.57009
DOI: 10.1016/0022-1236(92)90036-I
author: Varghese Mathai
author: A. L. Carey
published in: Journal of Functional Analysis
publication date: 1993-05-02T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 57Q10
zbMATH DE Number: 152030
zbMATH Keywords: \(L^ 2\)-Reidemeister-Franz torsion
zbMATH Keywords: Hilbert chain complex
zbMATH Keywords: Fuglede- Kadison determinant
reviewed by: Wolfgang Lück
MaRDI profile type: Publication
cites work: Q4086472
cites work: Q4204812
cites work: Analytic torsion and the heat equation
cites work: Q3721357
cites work: Bounds on the von Neumann dimension of \(L^ 2\)-cohomoloy and the Gauss- Bonnet theorem for open manifolds
cites work: \(L_ 2\)-cohomology and group cohomology
cites work: VON NEUMANN DIMENSION AND THE HOMOLOGY OF COVERING SPACES
cites work: Q5676841
cites work: Q3927697
cites work: De Rham-Hodge theory for \(L^2\)-cohomology of infinite coverings
cites work: Q3475762
cites work: Analytic torsion and closed geodesics on hyperbolic manifolds
cites work: Q3756189
cites work: Determinant theory in finite factors
cites work: \(L^ 2\)-analytic torsion
cites work: Q3350322
cites work: Whitehead torsion
cites work: Hyperbolic geometry: The first 150 years
cites work: Analytic torsion and R-torsion of Riemannian manifolds
cites work: Q3293867
cites work: R-torsion and the Laplacian on Riemannian manifolds
cites work: Q5180619
cites work: Q3888019
cites work: Q3633581
full work available at URL: 0022-1236(92)90036-i
OpenAlex ID: W2010518313
Wikidata QID: Q126282050
description: scientific article; zbMATH DE number 152030