Kinks and topology change

We show that if a change of spatial topology is mediated by a spacetime with an everywhere-non-singular metric of Lorentzian signature which admits a spinor structure, then the Kervaire semicharacteristic of the boundary plus the kink number of the Lorentzian metric on the boundary must vanish modulo 2. The kink number is a measure of how many times the light cone tips over on the boundary. It vanishes if the boundary is everywhere spacelike. This result gives a generalization of a previous selection rule: The number of wormholes plus the number of kinks created during a topology change is conserved modulo 2.