The index of Callias-type operators with Atiyah-Patodi-Singer boundary conditions

TL;DR

This paper extends the classical Callias-type index theorem to manifolds with compact boundary by computing the index of Callias-type operators with APS boundary conditions in terms of induced operators on a hypersurface.

Contribution

It generalizes the Callias-type index theorem to include manifolds with boundary and relates the index to operators on a hypersurface.

Findings

Derived a formula for the index with APS boundary conditions

Connected the index to induced operators on a hypersurface

Extended classical index theorem to manifolds with boundary

Abstract

We compute the index of a Callias-type operator with APS boundary condition on a manifold with compact boundary in terms of combination of indexes of induced operators on a compact hypersurface. Our result generalizes the classical Callias-type index theorem to manifolds with compact boundary.