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

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.

13 pages; v3: slightly shortened version, minor modifications

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