A Cheeger-Müller Theorem for Delocalized L2-analytic Torsion Form

Abstract

In this paper we define the delocalized L²-analytic torsion form and the delocalized L²-combinatorial torsion form. By using the method of Bismut-Goette, under the conditions of positive Novikov-Shubin invariants, nontrivial finite conjugacy class and the existence of a family of fiberwise Morse functions whose gradient fields satisfy the Thom-Smale transversality condition in every fiber, we prove the Cheeger-Müller type relation between the delocalized L²-analytic torsion form and the delocalized L²-combinatorial torsion form.