L^2 torsion without the determinant class condition and extended L^2 cohomology
| dc.creator | Braverman, M. | |
| dc.creator | Carey, A. | |
| dc.creator | Farber, M. | |
| dc.creator | Mathai, V. | |
| dc.date | 2004-06-10 | |
| dc.date.accessioned | 2026-07-07T06:21:39Z | |
| dc.date.available | 2026-07-07T06:21:39Z | |
| dc.description | 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^2 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. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406222 | |
| dc.identifier | http://arxiv.org/abs/math/0406222 | |
| dc.identifier | Commun. in Contemporary Math. vol. 7 no. 4 (2005) 421-462 | |
| dc.identifier | doi:10.1142/S0219199705001866 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95666 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Topology | |
| dc.title | L^2 torsion without the determinant class condition and extended L^2 cohomology | |
| dc.type | text |