Toeplitz operators and the full asymptotic torsion forms

Abstract

This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles {Fp}p∈N⁎. 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.