GROUP ACTIONS WITH TOPOLOGICALLY STABLE MEASURES

Differentiable Classification of Some Topologically Linear Actions

Let G act smoothly on S with fixed point set diffeomorphic to S O^kt^n — 3, and with all other orbits of the same type and of dimension r. Connell, Montgomery and Yang have shown that the action of G is topologically equivalent to a linear action of S if n —r^5. The problem then arises as to what can be said about the differentiable classification of these topologically linear actions. In some ...

Picard Groups of Topologically Stable Poisson Structures

We compute the group of Morita self-equivalences (the Picard group) of a Poisson structure on an orientable surface, under the assumption that the degeneracies of the Poisson tensor are linear. The answer involves mapping class groups of surfaces, i.e., groups of isotopy classes of diffeomorphisms. We also show that the Picard group of these structures coincides with the group of outer Poisson ...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Group Actions

The symmetric groups Sn, alternating groups An, and (for n ≥ 3) dihedral groups Dn behave, by their very definition, as permutations on certain sets. The groups Sn and An both permute the set {1, 2, . . . , n} and Dn can be considered as a group of permutations of a regular n-gon, or even just of its n vertices, since rigid motions of the vertices determine where the rest of the n-gon goes. If ...

Group Actions

There are a number of results of group theory presented in Herstein [1] (the counting principles in Sections 2.5 and 2.11, Cayley’s theorem in Section 2.9 and the Sylow theorems of Section 2.12, among others) whose proofs follow similar ideas. However, it is not apparent that this is so. This handout covers the ideas necessary to tie these results together. The important idea is that of an acti...