Toeplitz operators and the full asymptotic torsion forms

TL;DR

This paper investigates the detailed asymptotic expansion of analytic torsion forms for flat bundles, establishing the full expansion and deriving formulas for sub-leading terms, extending prior work on leading terms.

Contribution

It provides the first complete asymptotic expansion of torsion forms and explicitly computes the sub-leading term, advancing understanding beyond the leading order.

Findings

Proved the existence of the full asymptotic expansion.

Derived a formula for the sub-leading term.

Extended previous results on the first-order expansion.

Abstract

This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles. We prove the existence of the full expansion and give a formula for the sub-leading term, while Bismut-Ma-Zhang have studied the first-order expansion and expressed the leading term as the integral of a locally computable differential form.