Non-ergodicity on the SU(2)-character varieties

Fayssal Saadi

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arXiv · 2404.00372

Non-ergodicity on the SU(2)-character varieties

Fayssal Saadi

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Abstract

We describe the dynamics of a group $\Gamma$ 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 $\Gamma$-invariant rational functions on the representation variety of the genus two closed surface $S_2$ for some pair of multi-curves. We establish a similar result for the SU(2)-character variety of genus four non-orientable surfaces $N_4$ for some family of filling curves.

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Fayssal Saadi. 2024-03-30. Non-ergodicity on the SU(2)-character varieties. https://arxiv.org/abs/2404.00372

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