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The mapping class group action on
$\mathsf{SU}(3)$-character varieties
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 41 / Issue 8 / August 2021
- Published online by Cambridge University Press:
- 15 June 2020, pp. 2382-2396
- Print publication:
- August 2021
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- Article
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- You have access
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Let
$\unicode[STIX]{x1D6F4}$ be a compact orientable surface of genus 
$g=1$ with 
$n=1$ boundary component. The mapping class group 
$\unicode[STIX]{x1D6E4}$ of 
$\unicode[STIX]{x1D6F4}$ acts on the 
$\mathsf{SU}(3)$-character variety of 
$\unicode[STIX]{x1D6F4}$. We show that the action is ergodic with respect to the natural symplectic measure on the character variety.
