AN ANOMALY FORMULA FOR L²-ANALYTIC TORSIONS ON MANIFOLDS WITH BOUNDARY

We extend the definition, in the extended cohomology framework, of the L²- analytic torsion for covering spaces due to Braverman-Carey-Farber-Mathai to the case of manifolds with boundary, and prove an associated anomaly formula. Our main result may be viewed as a common generalization of the anomaly formula for Ray-Singer analytic torsion for manifolds with boundary proved by Brüning-Ma, as well as the anomaly formula for L²-analytic torsions for closed manifolds proved by Zhang. It generalizes also an earlier result of Lück-Schick, without the assumptions on the unitary representations as well as the technical “determinant class condition”.