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Conformal mapping

  1. Mar 12, 2010 #1
    how do we describe the biholomorphic self maps of the multiply puncture plane onto itself?
    I mean C\{pi,p2,p3..pn}

    Plane with n points taken away.

    I wanted to generailze the result for the conformal self maps of the punctured plane, but I do feel these are quite different animals.
    I thank you for any help/suggestions
  2. jcsd
  3. Mar 13, 2010 #2
    The singularities (and infinity) are removable. So you need to map the sphere to itself (az+b)/(cz+d) in such a way that you permute the points [itex]\{p_1,\dots,p_n,\infty\}[/itex].
    Last edited: Mar 13, 2010
  4. Mar 13, 2010 #3
    I thank you edgar,

    I think I see it now. So I suspect we get the full symmetric group on n letters then, as the automorphism group. Thank you again
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