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A locally conformally symplectic structure on Kerr space-time

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arxiv 2212.08210 v2 pith:PA6BJM7O submitted 2022-12-16 math.DG math.SG

classification math.DGmath.SG
keywords conformallylocallysymplectickerrstructuresystemcartercartesian
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R Kerr's Ricci-flat Lorentz 4-manifold was shown by B Carter in 1968 to support a classically completely integrable system of geodesics; here we interpret this system in terms of a locally conformally symplectic structure, which we identify (\S 2.2) using characteristic classes defined by Kerr-Schild Cartesian coordinates (regarded as a map to the Cayley-Penrose compactification of Minkowski space). This leads to the definition of an interesting cobordism category of contact 3-manifolds and 4-dimensional locally conformally symplectic cobordisms between them.

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  1. Boundary framings for locally conformally symplectic four-manifolds

    math.AT 2025-02 reject novelty 5.0 of 10

    The paper proposes a rational homotopy model for a classifying space of locally conformally symplectic four-manifolds and a cobordism category of three-manifolds with Omega^2 S^2-bundle framings, but the standalone te...

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