Communications in Mathematical Physics

, Volume 148, Issue 2, pp 345–352 | Cite as

Selection rules for topology change

  • G. W. Gibbons
  • S. W. Hawking


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 Σ which determines whether Σ 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 Σ and find that it is the mod2 Kervaire semi-characteristic.


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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • G. W. Gibbons
    • 1
  • S. W. Hawking
    • 1
  1. 1.D.A.M.T.P.CambridgeUK

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