Mathematics:
The genus of a surface is a topological invariant that is (roughly) the number of holes in the surface, usually denoted as g. For example, the genus of a coffee cup or a torus is 1, whilst the genus of a sphere is 0.
It is related to the Euler characteristic by the formula χ = 2 - 2g.
Strictly speaking, the genus is the number of non-intersecting closed curves that can be embedded in a surface without dividing it up.