Euler characteristic
Another generalization of the concept of Euler characteristic on manifolds comes from orbifolds (see Euler characteristic of an orbifold). While every manifold has an integer Euler characteristic, an orbifold can have a fractional Euler characteristic. For example, the teardrop orbifold has Euler characteristic 1 + 1/"p", where "p" is a prime number corresponding to the cone angle 2"" / "p".