An index formula on manifolds with fibered cusp ends

Abstract

We consider a compact manifold whose boundary is a locally trivial fiber bundle and an associated pseudodifferential algebra that models fibered cusps at infinity. Using trace-like functionals that generate the 0-dimensional Hochschild cohomology groups, we express the index of a fully elliptic fibered cusp operator as the sum of a local contribution from the interior and a term that comes from the boundary. This answers the index problem formulated by Mazzeo and Melrose. We give a more precise answer in the case where the base of the boundary fiber bundle is the circle. In particular, for Dirac operators associated to a "product fibered cusp metric", the index is given by the integral of the Atiyah-Singer form in the interior minus the adiabatic limit of the eta invariant of the restriction of the operator to the boundary.

22 pages. Prepublication du Laboratoire Emile Picard n.253. See also http://picard.ups-tlse.fr

References in corpus (3)

• Homology of pseudodifferential operators I. Manifolds with boundary
• An L^2-Index Theorem for Dirac Operators on S^1 * R^3
• Adiabatic limits of eta and zeta functions of elliptic operators

Cited by in corpus (2)

• Gravitational and axial anomalies for generalized Euclidean Taub-NUT metrics
• On the Homotopy Classification of Elliptic Operators on Manifolds with Edges