Involutions on Homotopy Spheres.
The standard P. A. Smith theory of p-group actions on spheres, disks, and euclidean spaces is extended to the case of p-group actions on tori (i.e., products of circles) and coupled with topological surgery theory to give a complete topological classification, valid in all dimensions, of the locally linear, orientation-reversing, involutions on tori with fixed point set of codimension one.
We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.