This number is an invariant for geometric objects belonging to a prescribed category that are equivalent in that category.  F
This number is an invariant for geometric objects belonging to a prescribed category that are equivalent in that category.  For smooth manifolds, it is defined as the number of signed zeroes of a generic tangent vector-field with isolated zeroes. For topological manifolds, it is the alternating sum of dimensions of the homology groups for the homology with coefficients in a field.  Defining a value that is, for polyhedra, the number of its vertices minus the number of its sides plus the number of its faces, FTP, identify this mathematical term named for an 18th-century Swiss mathematician.
This number is an invariant for geometric objects belonging to a prescribed category that are equivalent in that category.  
Euler characteristic or Euler number