Complex-valued Ray–Singer torsion

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• 作者：Dan Burghelea ; Stefan Haller
• 关键词：Ray– ; Singer torsion ; Reidemeister torsion ; Analytic torsion ; Combinatorial torsion ; Anomaly formula ; Bismut– ; Zhang ; Cheeger ; Mü ; ller theorem ; Euler structures ; Co-Euler structures ; Asymptotic expansion ; Heat kernel ; Dirac operator
• 刊名：Journal of Functional Analysis
• 出版年：2007
• 出版时间：1 July 2007
• 年：2007
• 卷：248
• 期：1
• 页码：27-78
• 全文大小：444 K

文摘

In the spirit of Ray and Singer we define a complex-valued analytic torsion using non-selfadjoint Laplacians. We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally this analytically defined invariant computes the complex-valued Reidemeister torsion, including its phase. We establish this conjecture in some non-trivial situations.