Inductive Limits of Area-Preserving Diffeomorphism Groups

A compact oriented surface with a given area form is considered. For each coordinate domain, we take the group of diffeomorphisms supported in this domain and preserving the area form. Finally, consider codimension $1$ normal subgroups in these groups. For each pair of coordinate domains one of which contains the closure of the other, there is an obvious inclusion of the corresponding groups. We describe the inductive limits (amalgams) of these two families of groups.