Subdivide Surface Modifier messes up concave shape I encountered a problem while modelling a toothed shape. When I applied the Subdivision Surface Modifier and added the supporting geometry so it doesn't look all that distorted, two additional pieces of surface stretched over the spaces between the teeth. 
It seems there is a connection between the left and right edge and the middle vertex which I can't select and edit.
I'd try to recreate your mesh, as it's easier to do so as fix your mesh.
Create a rectangular plane and use loop subdivide, using ctrl-R + Mousewheel. 



With this basic mesh, consisting only of quads, and the loop subdivide technique, it should be easy for you to use the subsurf modifier.