Hello,
The mapping between parent and child mesh vertices (and cells) is built when building the MeshView object. You can access these from the topology of your submesh :
submesh.topology().mapping()[mesh.id()].vertex_map()
submesh.topology().mapping()[mesh.id()].cell_map()
Note : In your code you redefine the variable marker after having marked your entities, making it zero for all entities so I suspect your submesh to be empty.