Ray-Singer type theorem for the refined analytic torsion (Q868931)

It is shown that the refined analytic torsion (math. DG/0505537) is a holomorphic section of the determinant line bundle over the space of complex representations of the fundamental group of a close oriented odd-dimensional manifold. The ratio with the Farber-Turaev torsion [\textit{V. G. Turaev}, Introduction to combinatorial torsions. Basel: Birkhäuser (2001; Zbl 0970.57001); \textit{M. Farber}, Math. Z. 234, No. 2, 339--349 (2000; Zbl 0955.57022)] is established. This allows to study the spectral flow using methods of combinatorial topology.