2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110330We show that the refined analytic torsion is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a closed oriented odd dimensional manifold. Further, we calculate the ratio of the refined analytic torsion and the Farber-Turaev combinatorial torsion. As an application, we establish a formula relating the eta-invariant and the phase of the Farber-Turaev torsion, which extends a theorem of Farber and earlier results of ours. This formula allows to study the spectral flow using methods of combinatorial topology.To appear in Journal of Functional Analysis The definition of the refined torsion was slightly changed, which made it more invariant, some references and remarks are addedDifferential GeometryMathematical PhysicsGeometric Topologytext