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A The Topology of Spacetime

  1. Apr 5, 2016 #1
    I watched this video : https://www.youtube.com/watch?v=sOiifkFYck4
    Here, the lecturer said that if someone wants a spacetime which contains spin structure (physically equal to the existence of fermions, CMIIW) should topologically ℝ×Σ, where Σ is the Cauchy surface.

    Is that true? If so, then singularities and fermions can't co-exist in the same universe, which lead us to a paradox, right?
    Anybody could give me some papers related to this topic please?
  2. jcsd
  3. Apr 5, 2016 #2


    Staff: Mentor

    I'm not sure; I'm not familiar with any papers on the subject. However, it seems plausible.

    Why not? There are spacetimes with singularities that have topology ##R \times \Sigma##, where ##\Sigma## is a 3-manifold. The simplest example is FRW spacetime.


    If it's true (and I'm not sure it is, see above), it is only a paradox if you think our actual universe contains singularities; I take it we agree that it contains fermions. :wink: But we don't know that that's the case.
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