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Is Horn-torus a valid genus-1 Riemann Surface?

  1. May 17, 2012 #1
    The plot below is a horn torus. Is that a valid genus-1 normal Riemann surface? I believe it is but I'm just a novice. I'm unsure about the single point in the center and if it "technically" still has a hole in it. Maybe I need to review that.
     

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  2. jcsd
  3. May 17, 2012 #2

    quasar987

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    A Riemann surface is, in particular, a 2 dimensional topological manifold. At the single point at the center, this space looks like 2 cones with their tips touching. Because of that, The horned torus is not a manifold and hence not a Riemann surface.
     
  4. May 18, 2012 #3
    Ok, thanks.
     
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