Geometric Residue Theorems for Bundle Maps

TL;DR

This paper develops geometric residue theorems for bundle maps over compact manifolds, linking residues to singularity submanifolds across various geometric contexts.

Contribution

It introduces a unified residue theory for bundle maps applicable to multiple types of singularities and geometric settings.

Findings

Residues are associated with singularity submanifolds for invariant polynomials.

The theory applies to smooth maps, CR-singularities, and spinor bundle maps.

Provides a new framework for analyzing singularities in differential geometry.

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.