On a road to nowhere: a folded universe can touch itself only in four dimensions

If CPT holds of the universe and not only of its laws, spacetime is two sheets joined at the Big Bang. Wherecan a point reach its own image on the other sheet? Outside any horizon, nowhere: the two are spacelikeseparated and the cross-sheet commutator vanishes identically. Inside a black hole the answer turns on twodistances: the half-turn round the sphere the fold demands, and how far round a falling path can actuallyget. Four spacetime dimensions is the only case in which the second is the larger, and contact then fills theregion inside half the horizon radius. Five dimensions fall short by exactly nothing. The region so selectedcarries closed timelike curves, and the image stress defocuses them.