Homeomorphic Type

The following three pieces of information completely determine the homeomorphic type of the surface (Massey 1967):

1. Orientability,

2. Number of boundary components,

3. Euler Characteristic.

See also Algebraic Topology, Euler Characteristic

References

Massey, W. S. Algebraic Topology: An Introduction. New York: Springer-Verlag, 1996.