Point defects topological charges

Suppose a two-dimensional vector field n is defined on a closed surface with Euler characteristic E. This field might contain point defects whose topological charges are defined as... 

The condition (i) implies that the modulus VFi vanishes at the centre of the spiral. Thus the centre of the spiral is a singular point of the structure as the phase of oscillations cannot be defined at this point. The latter is called a topological defect and possesses a topological charge equal to m. In the sequel, we consider only spirals for which m = lorm = -l, i.e., one-arm spirals, respectively left-handed or right-handed. 

---