REGULARITY OF THE ANALYTIC TORSION FORM ON FAMILIES OF NORMAL COVERINGS

摘要

We prove the smoothness of the L-2-analytic torsion form for fiber bundles with positive Novikov-Shubin invariant. We do so by generalizing the arguments of Azzali, Goette and Schick to an appropriate Sobolev space, and proving that the Novikov-Shubin invariant is also positive in the Sobolev setting, using an argument of Alvarez Lopez and Kordyukov.