## On Carvalho’s $K$-theoretic formulation of the cobordism invariance of the index

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**134**(2006), 3395-3404 Request permission

## Abstract:

We give an analytic proof of the fact that the index of an elliptic operator on the boundary of a compact manifold vanishes when the principal symbol comes from the restriction of a $K$-theory class from the interior. The proof uses non-commutative residues inside the calculus of cusp pseudodifferential operators of Melrose.## References

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## Additional Information

**Sergiu Moroianu**- Affiliation: Institutul de Matematică al Academiei Române P.O. Box 1-764, RO-014700 Bucharest, Romania
- Email: moroianu@alum.mit.edu
- Received by editor(s): November 19, 2004
- Received by editor(s) in revised form: May 11, 2005
- Published electronically: May 11, 2006
- Additional Notes: This research was partially supported by RTN HPRN-CT-2002-00280 “Quantum Spaces – Noncommutative Geometry” and Marie Curie MERG 006375 funded by the European Commission, and by a CERES contract (2004)
- Communicated by: Mikhail Shubin
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**134**(2006), 3395-3404 - MSC (2000): Primary 58J20, 58J42
- DOI: https://doi.org/10.1090/S0002-9939-06-08347-X
- MathSciNet review: 2231925