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 Z2 invariant for a closed oriented 3-manifold-SIGMA which determines whether SIGMA can be the spacelike boundary of a compact manifold M which admits a Lorentzian metric and a spinor structure. We evaluate this invariant in terms of the homology groups of SIGMA and find that it is the mod2 Kervaire semi-characteristic.