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Vertex of Fundamental Domains & Elliptic Points

  1. Apr 25, 2012 #1
    Dear Folks:
    Suppose [itex]\Gamma[/itex] is a discrete subgroup of SL2(R), which acts on the upper half complex plane as Mobius transformation. F is its fundamental domain. If z is a vertex of F which does not lie on the extended real line ( that is R[itex]\bigcup[/itex][itex]\infty[/itex] ) ,then must x be an elliptic point?? Many thanks!!
    For example, if [itex]\Gamma[/itex] is SL2(Z), then x is either ei[itex]\frac{2}{3}[/itex][itex]\pi[/itex] or ei[itex]\frac{4}{3}[/itex][itex]\pi[/itex], both of them are elliptic points.
     
  2. jcsd
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