Geometric Residue Theorems for Bundle Maps

Abstract

In this paper we prove geometric residue theorems for bundle maps over a compact manifold. The theory developed associates residues to the singularity submanifolds of the map for any invariant polynomial. The theory is then applied to a variety of settings: smooth maps between equidimensional manifolds, CR-singularities, finite singularities and singularities of odd forms as spinor bundle maps.