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

Published electronically:
October 3, 2001

MathSciNet review:
1873784

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Abstract | References | Similar Articles | Additional Information

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