  We are interested in the 3-Calabi-Yau categories $\mathcal{D}$ arising from
quivers with potential associated to a triangulated marked surface $\mathbf{S}$
(without punctures). We prove that the spherical twist group ST of
$\mathcal{D}$ is isomorphic to a subgroup (generated by braid twists) of the
mapping class group of the decorated marked surface
$\mathbf{S}_{\bigtriangleup}$. Here $\mathbf{S}_{\bigtriangleup}$ is the
surface obtained from $\mathbf{S}$ by decorating with a set of decorated
points, where the number of points equals the number of triangles in any
triangulations of $\mathbf{S}$. For instance, when $\mathbf{S}$ is an annulus,
the result implies the corresponding spaces of stability conditions on
$\mathcal{D}$ is contractible.
