Exotic iterated Dehn twists

Consider cotangent bundles of exotic spheres with their canonical symplectic structure. They admit automorphisms that preserve the part at infinity of one fiber and which are analogous to the square of a Dehn twist. Pursuing that analogy, we show that they have infinite order up to isotopy (inside the group of all automorphisms with the same behavior).Simons Foundation (Simons Investigator Grant)National Science Foundation (U.S.) (Grant DMS-1005288