Nils Waterstraat
Abstract
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We give a short proof of the Morse index theorem for geodesics in semi-Riemannian manifolds by using K 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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We give a short proof of the Morse index theorem for geodesics in semi-Riemannian manifolds by using K K -theory. This makes the Morse index theorem reminiscent of the Atiyah-Singer index theorem for families of selfadjoint elliptic operators.
Key concepts: Morse code, Atiyah–Singer index theorem, Geodesic, Index (typography), Mathematics, Semantics (computer science), Algebra over a field, Pure mathematics