2D vector field defects with winding numbers n = +1, −1, +2
The winding number n = (1/2π)∮∇θ·dl counts how many times the field direction rotates around a closed loop. Topological defects are stable because removing them requires infinite energy. For a defect pair with opposite winding numbers (n = +1 and n = −1), the total charge is conserved; they can annihilate pairwise. In liquid crystals, defect charges determine textures; in superfluids, quantized vortices carry one unit of circulation.