A remark on the action of the mapping class group on the unit tangent bundle

Souto, J.

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 3-4, pp. 589-601.

On montre que l’action standard du groupe modulaire $\mathrm{Map}\left(\Sigma \right)$ d’une surface $\Sigma$ de genre assez grand sur le fibré unitaire tangent $T^1\Sigma$ n’est pas homotopique à une action lisse.

We prove that the standard action of the mapping class group $\mathrm{Map}\left(\Sigma \right)$ of a surface $\Sigma$ of sufficiently large genus on the unit tangent bundle $T^1\Sigma$ is not homotopic to any smooth action.

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