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arXiv · 2105.11985

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

Martin Puchol·Yeping Zhang·Jialin Zhu
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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-M\"uller/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.

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Martin Puchol, Yeping Zhang, Jialin Zhu. 2021-05-25. A comparison between the Bismut-Lott torsion and the Igusa-Klein torsion. https://arxiv.org/abs/2105.11985

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