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Rotation number and lifts of a Fuchsian action of the modular group on the circle

We characterize the semi-conjugacy class of a Fuchsian action of the modular group on the circle in terms of rotation numbers of two standard generators and that of their product. We also show that among lifts of a Fuchsian action of the modular group, only 5-fold lift admits a similar characterization. These results indicate similarity and difference between rotation number and linear character.

preprint2015arXivOpen access
Yoshifumi Matsuda
math.GRmath.DSmath.GT
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Yoshifumi Matsuda

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