A Cheeger-Müller Theorem for Delocalized L^(2)-analytic Torsion Form  

作　　者：Guo Lin AN 

机构地区：[1]Chern Institute of Mathematics and LPMC,Nankai University,Tianjin,300071,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第11期2615-2670,共56页数学学报（英文版）

基　　金：Supported by Nankai Zhide Foundation。

摘　　要：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.

关 键 词：Delocalized trace Novikov-Shubin invariant delocalized L^(2)-analytic torsion form delocalized L^(2)-combinatorial torsion form 

分 类 号：O186.12[理学—数学]