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Selection rules for topology change

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Abstract

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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  1. D.A.M.T.P., Silver Street, CB3 9EW, Cambridge, UK

    G. W. Gibbons & S. W. Hawking

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  1. G. W. Gibbons
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  2. S. W. Hawking
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Communicated by N. Yu. Reshetikhin

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Gibbons, G.W., Hawking, S.W. Selection rules for topology change. Commun.Math. Phys. 148, 345–352 (1992). https://doi.org/10.1007/BF02100864

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  • DOI: https://doi.org/10.1007/BF02100864

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