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- W3100142664 abstract "Let (X m+1, g) be a globally hyperbolic spacetime with Cauchy surface diffeomorphic to an open subset of $${mathbb{R}^{m}}$$ . The Legendrian Low conjecture formulated by Natário and Tod says that two events $${x, y in X}$$ are causally related if and only if the Legendrian link of spheres $${{mathfrak{S}_x,,mathfrak{S}_y}}$$ whose points are light geodesics passing through x and y is non-trivial in the contact manifold of all light geodesics in X. The Low conjecture says that for m = 2 the events x, y are causally related if and only if $${{mathfrak{S}_x,,mathfrak{S}_y}}$$ is non-trivial as a topological link. We prove the Low and the Legendrian Low conjectures. We also show that similar statements hold for any globally hyperbolic (X m+1, g) such that a cover of its Cauchy surface is diffeomorphic to an open domain in $${mathbb{R}^{m}}$$ ." @default.
- W3100142664 created "2020-11-23" @default.
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- W3100142664 date "2009-12-15" @default.
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- W3100142664 title "Legendrian Links, Causality, and the Low Conjecture" @default.
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- W3100142664 doi "https://doi.org/10.1007/s00039-009-0039-x" @default.
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