Symplectic automorphisms of T^*S^2

Abstract: 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 �. 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.

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