  Let M be the cotangent bundle of S^2, with the standard symplectic structure.
By adapting an argument of Gromov we determine the weak homotopy type of the
group S of those symplectic automorphisms of M which are trivial at infinity.
It turns out that S is weakly homotopy equivalent to \Z. \pi_0(S) is generated
by the class of the standard "generalized Dehn twist". As a consequence, we
show that there are different connected components of S which lie in the same
connected component of the corresponding group of diffeomorphisms.
