Selection rules for topology change

It is shown that there are restrictions on the possible changes of topology of space sections of the universe if this topology change takes place in a compact region which has a Lorentzian metric and spinor structure. In particular, it is impossible to create a single wormhole or attach a single handle to a spacetime but it is kinematically possible to create such wormholes in pairs. Another way of saying this is that there is a ₂ invariant for a closed oriented 3-manifold which determines whether can be the spacelike boundary of a compact manifoldM which admits a Lorentzian metric and a spinor structure. We evaluate this invariant in terms of the homology groups of and find that it is the mod2 Kervaire semi-characteristic.