Automorphisms of character varieties

Marché, Julien; Simon, Christopher-Lloyd

Annales Henri Lebesgue, Tome 4 (2021), pp. 591-603.

Nous montrons que le groupe d’automorphismes de la variété des ${\mathrm{SL}}_2\left(ℂ\right)$ caractères d’une surface orientable close de caractéristique d’Euler strictement négative est une extension finie de son groupe modulaire. En cours de route, nous donnons une caractérisation simple des valuations de l’algèbre des fonctions sur la variété des caractères qui proviennent des laminations mesurées.

We show that the algebraic automorphism group of the ${\mathrm{SL}}_2\left(ℂ\right)$ character variety of a closed orientable surface with negative Euler characteristic is a finite extension of its mapping class group. Along the way, we provide a simple characterization of the valuations on the character algebra coming from measured laminations.

Classification : 57K20
Mots clés : mapping class group, character variety, measured lamination

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