Concerning the embedding in
the plane of homogeneous proper subcontinua of a 2-manifold, it is shown here that
there is an embedding if the continuum is decomposable and the manifold is
orientable. The embedding is obtained by constructing an annulus on the manifold
containing the continuum; in the nonorientable case an annulus or a Möbius strip
containing the continuum may be found. Similar results are obtained for
continua on a 2-manifold which have a decomposition into continua with zero
1-dimensional Betti numbers such that the decomposition space is a finite planar
graph.
