New proof of the cobordism invariance of the index

Braverman, Maxim

doi:10.1090/S0002-9939-01-06250-5

New proof of the cobordism invariance of the index
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by Maxim Braverman

Proc. Amer. Math. Soc. 130 (2002), 1095-1101

DOI: https://doi.org/10.1090/S0002-9939-01-06250-5

Published electronically: October 3, 2001

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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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