Ergodicity conjecture for non-extreme Euler-class components
Let be a closed surface of genus , let , and let be the Euler-class map on the representation space . For each integer with , consider the component .
Euler-component ergodicity conjecture. For each integer , the -action on the component of is ergodic.
The claim concerns the non-extreme components of the representation space, contrasting with the proper action on the extreme components corresponding to Teichmüller space. The source does not state whether this conjecture has been resolved.
References
Primary source
William M. Goldman, “Mapping Class Group Dynamics on Surface Group Representations”, arXiv:math/0509114 (2006).
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