In this paper we define the delocalized L^(2)-analytic torsion form and the delocalized L^(2)-combinatorial torsion form.By using the method of Bismut-Goette,under the conditions of positive Novikov-Shubin invariants,...In this paper we define the delocalized L^(2)-analytic torsion form and the delocalized L^(2)-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 L^(2)-analytic torsion form and the delocalized L^(2)-combinatorial torsion form.展开更多
文摘In this paper we define the delocalized L^(2)-analytic torsion form and the delocalized L^(2)-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 L^(2)-analytic torsion form and the delocalized L^(2)-combinatorial torsion form.
