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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Carvalho’s $K$-theoretic formulation of the cobordism invariance of the index
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by Sergiu Moroianu PDF
Proc. Amer. Math. Soc. 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.
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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