Exotic spheres and the topology of the symplectomorphism group.

We show that the Hamiltonian isotopy class of the symplectic Dehn twist depends on the parametrisation used in the construction. Moreover, this result is used to construct non-trivial symplectomorphisms of T^(S^n x S^1) having compact support, as well as non-standard symplectic structures on T^(S^n x S^1) coinciding with the standard structure outside of a compact set. (joint with Jonathan Evans)