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arXiv:1007.1190 [math.DG]AbstractReferencesReviewsResources

A K-Theoretic Proof of the Morse Index Theorem in Semi-Riemannian Geometry

Nils Waterstraat

Published 2010-07-07, updated 2012-06-14Version 3

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.

Comments: 13 pages; v3: slightly shortened version, minor modifications
Journal: Proc. Amer. Math. Soc. 140, 2012, 337-349
Categories: math.DG, math.SP
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