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Характеристические классы и теория пересечений
4 сентября 2014 г., г. Москва, ул. Усачева, д. 6., Факультет математики НИУ ВШЭ
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Dynamics of the mapping class group in character varieties of genus 2 surfaces
Julien Marché |
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Эта страница: | 89 |
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Аннотация:
The following question was popularized by Goldman: given a genus $g$ surface $S$ and a group $G$, the mapping class group $\text{Mod}(S)$ acts on the character variety $X(S,G)$ of conjugacy classes of representations of the fundamental group of $S$ into $G$. When G is compact, Goldman and Xia–Pickrell showed that the action is ergodic whereas when $G=\text{PSL}_2(R)$, some component of $X(S,G)$ is the Teichmuller space, and the action is proper and discontinuous. In a work with M. Wolff we prove that the action on the remaining components is ergodic. We will prove one case with techniques mixing hyperbolic and symplectic geometry.
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