Tohoku Mathematical Journal
2005
March
SECOND SERIES VOL. 57, NO. 1

Tohoku Math. J.
57 (2005), 23-43

Title THE ORDER OF PERIODIC ELEMENTS OF TEICHMÜLLER MODULAR GROUPS

Author Ege Fujikawa

(Received May 2, 2003, revised March 10, 2004)
Abstract. 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 Teichmuller modular group. We may also estimate the order of the period.

2000 Mathematics Subject Classification. Primary 30F60; Secondary 30C62.

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