  As shown by Louko and Sorkin in 1995, topology change in Lorentzian signature
involves spacetimes with singular points, which they called crotches. We modify
their construction to obtain Lorentzian semiclassical wormholes in
asymptotically AdS. These solutions are obtained by inserting crotches on known
saddles, like the double-cone or multiple copies of the Lorentzian black hole.
The crotches implement swap-identifications, and are classically located at an
extremal surface. The resulting Lorentzian wormholes have an instanton action
equal to their area, which is responsible for topological suppression in any
number of dimensions. We conjecture that including these Lorentzian wormhole
spacetimes is gauge-equivalent to path integrating over all mostly Euclidean
smooth spacetimes. We present evidence for this by reproducing semiclassical
features of the genus expansion of the spectral form factor, and of a late-time
two point function, by summing over the moduli space of Lorentzian wormholes.
As a final piece of evidence, we discuss the Lorentzian version of West-Coast
replica wormholes.
