ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS

Abstract

We use Toeplitz operators to evaluate the leading term in the asymptotics of the analytic torsion forms associated with a family of flat vector bundles Fp. For p ∞ N, the flat vector bundle Fp is the direct image of Lp, where L is a holomorphic positive line bundle on the fibres of a flat fibration by compact Kähler manifolds. The leading term of the analytic torsion forms is the integral along the fibre of a locally defined differential form.