  The refined analytic torsion, defined by M. Braverman and T. Kappeler on
closed manifolds, can be viewed as a refinement of the Ray-Singer torsion,
since it is a canonical choice of an element with Ray-Singer norm one, in case
of unitary representations. The complex phase of the refinement is given by the
rho-invariant of the odd-signature operator. Unfortunately there seems to be no
canonical way to extend the construction of Braverman and Kappeler to compact
manifolds with boundary. In particular a gluing formula seems to be out of
reach. We propose a different refinement of analytic torsion, similar to
Braverman and Kappeler, which does apply to compact manifolds with and without
boundary. In a subsequent publication we establish a gluing formula for our
construction, which in fact can also be viewed as a gluing law for the original
definition of refined analytic torsion by Braverman and Kappeler.

Differential Geometry