Poincaré - Reidemeister metric, Euler structures, and torsion
| dc.creator | Farber, Michael | |
| dc.creator | Turaev, Vladimir | |
| dc.date | 1998-03-27 | |
| dc.date | 1998-05-16 | |
| dc.date.accessioned | 2026-07-07T05:24:13Z | |
| dc.date.available | 2026-07-07T05:24:13Z | |
| dc.description | In this paper we define a Poincaré-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial "torsion-type" invariant which refines the PR-metric, introduced earlier by the first author, and contains an additional sign or phase information. We compute the PR-scalar product in terms of the torsions of Euler structures, introduced earlier by the second author. We show that the sign of our PR-scalar product is determined by the Stiefel-Whitney classes and the semi-characteristic of the manifold. As an application, we compute the Ray-Singer analytic torsion via the torsions of Euler structures. Another application: a computation of the twisted semi-characteristic in terms of the Stiefel-Whitney classes. | |
| dc.description | 3 figures, AmsTex; Theorems 4.4 and 11.2 improved | |
| dc.identifier | https://arxiv.org/abs/math/9803137 | |
| dc.identifier | http://arxiv.org/abs/math/9803137 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76754 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Topology | |
| dc.title | Poincaré - Reidemeister metric, Euler structures, and torsion | |
| dc.type | text |