Currently, the empty map is a cell decomposition of the sphere with one vertex and one face
sage: from combisurf import OrientedMap
sage: empty_map = OrientedMap("", "")
sage: empty_map.num_vertices()
1
sage: empty_map.num_faces()
1
sage: empty_map.euler_characteristic()
2
If we forced maps to be non-empty and connected, that might be a valid convention. However, we do have non-connected ones and this convention breaks terribly disjoint union: we do not have a way to express k disjoint spheres with a single vertex and no edge.
Proposal: make the empty map be the empty surface with no vertex, no face and Euler characteristic 0.
Currently, the empty map is a cell decomposition of the sphere with one vertex and one face
If we forced maps to be non-empty and connected, that might be a valid convention. However, we do have non-connected ones and this convention breaks terribly disjoint union: we do not have a way to express k disjoint spheres with a single vertex and no edge.
Proposal: make the empty map be the empty surface with no vertex, no face and Euler characteristic 0.