Rigidity aspects of a cosmological singularity theorem
This paper improves a singularity theorem by Galloway and Ling for globally hyperbolic spacetimes satisfying the null energy condition with 2-convex Cauchy surfaces, establishing that such spacetimes are either past null geodesically incomplete or possess specific topological structures (spherical spaces or surface bundles), while also relaxing convexity requirements under isometry and strengthening conclusions for non-orientable, non-prime, or specific Haken manifolds without needing finite covers.