Opérateurs de Toeplitz et torsion analytique asymptotique

Abstract

In this Note, we use the theory of Toeplitz operators to obtain the leading term in the asymptotic expansion of the analytic torsion forms associated with a family of flat vector bundles that are the direct image of L p , where L is a positive line bundle along the fibres of a flat fibration by compact Kähler manifolds. The leading term is given by the integral of locally computable differential forms.