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 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 L 2 cohomology. Under the determinant class assumption the L 2 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.
Original language | English |
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Pages (from-to) | 421-462 |
Number of pages | 42 |
Journal | Communications in Contemporary Mathematics |
Volume | 7 |
Issue number | 4 |
DOIs | |
Publication status | Published - Aug 2005 |