Refined Analytic Torsion
| dc.creator | Braverman, Maxim | |
| dc.creator | Kappeler, Thomas | |
| dc.date | 2005-05-25 | |
| dc.date | 2005-12-20 | |
| dc.date.accessioned | 2026-07-07T06:40:02Z | |
| dc.date.available | 2026-07-07T06:40:02Z | |
| dc.description | For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. The refined analytic torsion is a holomorphic function of the representation of the fundamental group. When the representation is unitary, the absolute value of the refined analytic torsion is equal to the Ray-Singer torsion, while its phase is determined by the eta-invariant. The fact that the Ray-Singer torsion and the eta-invariant can be combined into one holomorphic function allows to use methods of complex analysis to study both invariants. In particular, we extend and improve a result of Farber about the relationship between the Farber-Turaev absolute torsion and the eta-invariant. | |
| dc.description | Minor mistakes are corrected. Some notations are slightly improved. More details are given in the proof of Theorem 9.5 | |
| dc.identifier | https://arxiv.org/abs/math/0505537 | |
| dc.identifier | http://arxiv.org/abs/math/0505537 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101298 | |
| dc.subject | Differential Geometry | |
| dc.subject | Functional Analysis | |
| dc.title | Refined Analytic Torsion | |
| dc.type | text |