Refined analytic torsion on manifolds with boundary (Q1016794)

In a recent series of papers, \textit{M. Braverman} and \textit{T. Kappeler} introduced a refinement of the analytic torsion of Ray--Singer for closed manifolds [J. Differ. Geom. 78, No. 2, 193--267 (2008; Zbl 1147.58034), Int. Math. Res. Not. 2008, Article ID rnn030, 21 p. (2008; Zbl 1146.58023), Ann. Inst. Fourier 57, No. 7, 2361--2387 (2007; Zbl 1147.58033)]. The complex phase of the refinement is given by the rho-invariant of the odd-signature operator and therefore the refined torsion gives more geometric information than the original Ray--Singer torsion. In the present paper the author proposes a different refinement of the analytic torsion, which is similar in spirit to that of Braverman and Kappeler but has the advantage of being applicable to compact manifolds with boundary.