On the gluing formula of real analytic torsion forms

TL;DR

This paper extends the analytic torsion form to boundary cases and establishes a gluing formula for smooth fibrations with fiberwise Morse functions, assuming product metrics near the boundary.

Contribution

It introduces a boundary extension of the Bismut-Lott torsion form and proves a gluing formula under specific geometric conditions.

Findings

Extended torsion form to boundary cases

Proved gluing formula for fibrations with Morse functions

Assumed product structure near the boundary

Abstract

In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We assume that the metrics have product structures near the cutting hypersurface.