Kähler structures on ML

Jeudi 28 mai 2009 15:45-16:45 - Dumas David - Chicago

Résumé : The space $ML$ of measured geodesic laminations on a hyperbolic surface
$S$ has a natural symplectic structure, which was described by Thurston using train track coordinates. On the other hand, for any complex structure $X$ on $S$, there is a natural identification between $ML$ and the vector space $Q(X)$ of holomorphic quadratic differentials on $X$. We show that this identification is compatible with both the symplectic structure of $ML$ and the complex structure of $Q(X)$, inducing a (stratified, singular) Kähler structure on each of them.

Lieu : 425 - 121-123

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