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

Author: Sergiu Moroianu
Journal: Proc. Amer. Math. Soc. 134 (2006), 3395-3404
MSC (2000): Primary 58J20, 58J42
Published electronically: May 11, 2006
MathSciNet review: 2231925
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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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Sergiu Moroianu
Affiliation: Institutul de Matematică al Academiei Române P.O. Box 1-764, RO-014700 Bucharest, Romania

Keywords: Cusp pseudodifferential operators, noncommutative residues
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.