A skyrmion is a topologically protected spin texture with integer winding number Q. The topological charge Q = (1/4π)∫n·(∂ₓn × ∂ᵧn)dxdy counts how many times the spin field wraps around the sphere — it cannot be changed by smooth deformations.
Q = (1/4π) ∫∫ n⃗ · (∂ₓn⃗ × ∂ᵧn⃗) dx dy ∈ ℤ — Integer-valued, topologically protected