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

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

2010-07-07

arxiv.org/abs/1007.1190v2

Mathematics

Differential Geometry

15 Pages; v2: minor modifications

Scientific paper

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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