2008/10/31 by Vladimir Chernov, Stefan Nemirovski · 1 citation
Mathematics · Physics and Astronomy · #math.SG #gr-qc #math-ph #math.GT #math.MP #msc:57R17 #msc:53C50 #msc:53C80 #msc:57Q45 #msc:83C75
paper · pdf · doi:10.1007/s00039-009-0039-x
published as Geom. Funct. Anal. 19 (2010), 1320-1333 · Version 3 - minor improvements, references added 11 pages, 1 figure
Let (Xm+1, g) be a globally hyperbolic spacetime with Cauchy surface diffeomorphic to an open subset of \mathbb Rm. The Legendrian Low conjecture formulated by Natário and Tod says that two events x,y∈ß are causally related if and only if the Legendrian link of spheres \mathfrak Sx, \mathfrak Sy 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 Sx, \mathfrak Sy 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 (Xm+1, g) such that a cover of its Cauchy surface is diffeomorphic to an open domain in \mathbb Rm.