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New proof of the cobordism invariance of the index


Author: Maxim Braverman
Journal: Proc. Amer. Math. Soc. 130 (2002), 1095-1101
MSC (1991): Primary 32L20; Secondary 58G10, 14F17
DOI: https://doi.org/10.1090/S0002-9939-01-06250-5
Published electronically: October 3, 2001
MathSciNet review: 1873784
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Abstract: We give a simple proof of the cobordism invariance of the index of an elliptic operator. The proof is based on a study of a Witten-type deformation of an extension of the operator to a complete Riemannian manifold. One of the advantages of our approach is that it allows us to treat directly general elliptic operators which are not of Dirac type.


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Additional Information

Maxim Braverman
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email: maxim@neu.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06250-5
Keywords: Vanishing theorem, Clifford bundle, Dirac operator, Andreotti-Grauert theorem, Melin inequality
Received by editor(s): October 11, 2000
Published electronically: October 3, 2001
Additional Notes: This research was partially supported by grant No. 96-00210/1 from the United States-Israel Binational Science Foundation (BSF)
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2001 American Mathematical Society

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