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Type: Journal article
Title: L2 torsion without the determinant class condition and extended L2 cohomology
Author: Braverman, M.
Carey, A.
Farber, M.
Varghese, M.
Citation: Communications in Contemporary Mathematics, 2005; 7(4):421-462
Publisher: World Scientific Publ Co Pte Ltd
Issue Date: 2005
ISSN: 0219-1997
Statement of
Braverman, Maxim; Carey, Alan; Farber, Michael; Mathai, Varghese
Abstract: We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L<sup>2</sup> torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L<sup>2</sup> cohomology. Under the determinant class assumption the L<sup>2</sup> torsions of this paper specialize to the invariants studied in our previous work [6]. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler [3] we obtain a Cheeger–Müller type theorem stating the equality between the combinatorial and the analytic L<sup>2</sup> torsions.
Description: © World Scientific Publishing Company
DOI: 10.1142/S0219199705001866
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Pure Mathematics publications

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