A remark on the higher torsion invariants for flat vector bundles with finite holonomy

2022/03/04 by Lie Fu, Fu, Lie, Yeping Zhang +1
Mathematics · #57Q10 #58J52 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2203.02353

openalex publication_date 2022/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Igusa-Klein topological torsion and the Bismut-Lott analytic torsion are equivalent for any flat vector bundle whose holonomy is a finite subgroup of GL_n(ℚ). Our proof uses Artin's induction theorem in representation theory to reduce the problem to the special case of trivial flat line bundles, which is a recent result of Puchol, Zhu and the second author. The idea of using Artin's induction theorem appeared in a paper of Ohrt on the same topic, of which our present work is an improvement.

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