A comparison between the Bismut-Lott torsion and the Igusa-Klein torsion

2021/05/25 by Martin Puchol, Puchol, Martin, Yeping Zhang +3
Mathematics · #58J52 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2105.11985

openalex publication_date 2021/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a fibration with compact fiber together with a unitarily flat complex vector bundle over the total space. Under the assumption that the fiberwise cohomology admits a filtration with unitary factors, we construct Bismut-Lott analytic torsion classes. The analytic torsion classes obtained satisfy Igusa's and Ohrt's axiomatization of higher torsion invariants. As a consequence, we obtain a higher version of the Cheeger-Müller/Bismut-Zhang theorem: for trivial flat line bundles, the Bismut-Lott analytic torsion classes coincide with the Igusa-Klein higher topological torsions up to a normalization.

Citations

• Morse theory and higher torsion invariants II
• Adiabatic limit, Witten deformation and analytic torsion forms

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