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We describe the dynamics of a group generated by Dehn twists along two filling multi-curves or a family of filling curves on the SU (2) -representation variety of closed surfaces. Consequently, we provide explicit -invariant rational functions on the representation variety of the genus two closed surface S₂ for some pair of multi-curves. We establish a similar result for the SU (2) -character variety of genus four non-orientable surfaces N₄ for some family of filling curves.
Fayssal Saadi (Sat,) studied this question.