Annals of Global Analysis and Geometry

, Volume 52, Issue 4, pp 465–482 | Cite as

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

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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.

Keywords

Callias-type operator Atiyah–Patodi–Singer boundary condition Index theory 

Notes

Acknowledgements

I am very grateful to Prof. Maxim Braverman for bringing this problem to my attention and offering valuable suggestions. I would also like to thank Simone Cecchini and Chris Kottke for helpful discussions. Finally, I appreciate the constructive comments and suggestions by the reviewers.

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of MathematicsNortheastern UniversityBostonUSA

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