A comparison of the absolute and relative real analytic torsion forms

TL;DR

This paper compares absolute and relative real analytic torsion forms over fibrations with boundaries, establishing a comparison formula and confirming a conjectured gluing formula through advanced mathematical techniques.

Contribution

It introduces a new comparison formula for torsion forms and proves a conjectured gluing formula, advancing the understanding of analytic torsion in geometric analysis.

Findings

Established a comparison formula for torsion forms

Proved a version of the gluing formula conjectured by the author

Utilized a gluing formula by Puchol, Zhang, and the author

Abstract

In this paper we establish a comparison formula of the absolute and relative real analytic torsion forms over fibrations with boundaries. The key tool is a gluing formula of analytic torsion forms proved by M. Puchol, Y. Zhang and the author. As a consequence of the comparison formula, we prove another version of the gluing formula of the analytic torsion forms conjectured originally by the author.