The order of periodic elements of Teichmüller modular groups


We consider a quasiconformal automorphism of a Riemann surface, which fixes the homotopy class of a simple closed geodesic. Under certain conditions on the injectivity radius of the surface and bounds on the dilatation of the map, the automorphism induces a periodic element of the Teichmüller modular group. We may also estimate the order of the period.

submission: 19 October, 2003
revision: 13 October, 2004
to appear in Tohoku Math. J.

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