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A $ K$-theoretic proof of the Morse index theorem in semi-Riemannian geometry


Author: Nils Waterstraat
Journal: Proc. Amer. Math. Soc. 140 (2012), 337-349
MSC (2010): Primary 58E10; Secondary 58J20, 58J30, 34L40
DOI: https://doi.org/10.1090/S0002-9939-2011-10874-8
Published electronically: May 5, 2011
MathSciNet review: 2833544
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Abstract: We give a short proof of the Morse index theorem for geodesics in semi-Riemannian manifolds by using $ K$-theory. This makes the Morse index theorem reminiscent of the Atiyah-Singer index theorem for families of selfadjoint elliptic operators.


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Additional Information

Nils Waterstraat
Affiliation: Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstraße 3-5, D-37073 Göttingen, Germany
Email: waterstraat@web.de

DOI: https://doi.org/10.1090/S0002-9939-2011-10874-8
Received by editor(s): July 7, 2010
Received by editor(s) in revised form: October 28, 2010
Published electronically: May 5, 2011
Communicated by: Varghese Mathai
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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