Geodesic simplices in pseudo-hyperbolic space of signature (p,q) admit a cohomological interpretation with a necessary and sufficient condition for finite volume, implying every ideal geodesic polytope in signature (2,2) has finite volume.
Lorentz spacetimes of constant curvature
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Geodesic simplices of pseudo-hyperbolic space
Geodesic simplices in pseudo-hyperbolic space of signature (p,q) admit a cohomological interpretation with a necessary and sufficient condition for finite volume, implying every ideal geodesic polytope in signature (2,2) has finite volume.