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© World Scientific Publishing CompanyWe 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 L2 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 L2 cohomology. Under the determinant class assumption the L2 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 L2 torsions.Braverman, Maxim; Carey, Alan; Farber, Michael; Mathai, Varghes

L2 TORSION WITHOUT THE DETERMINANT CLASS CONDITION AND EXTENDED L2 COHOMOLOGY

L² TORSION WITHOUT THE DETERMINANT CLASS CONDITION AND EXTENDED L² COHOMOLOGY