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|Title:||L2 torsion without the determinant class condition and extended L2 cohomology|
|Citation:||Communications in Contemporary Mathematics, 2005; 7(4):421-462|
|Publisher:||World Scientific Publ Co Pte Ltd|
|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 . Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler  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|
|Appears in Collections:||Pure Mathematics publications|
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