The Atiyah-Patodi-Singer theorem for perturbed Dirac operators on even-dimensional manifolds with bounded geometry

摘要

This paper establishes conditions under which one can prove anAtiyah-Patodi-Singer index theorem for perturbed Dirac operators oncomplete noncompact even-dimensional manifolds with boundary. Thisindex theorem introduces into index theory spectral invariants ofself-adjoint perturbed Dirac operators on noncompact manifolds.