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

Waterstraat, Nils

doi:10.1090/S0002-9939-2011-10874-8

A $K$-theoretic proof of the Morse index theorem in semi-Riemannian geometry
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Proc. Amer. Math. Soc. 140 (2012), 337-349 Request permission

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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