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The theoretical research of the origin of magnetic skyrmion is veryinteresting. By using decomposition theory of gauge potential and the gaugeparallel condition of local bases of $su(2)$ Lie algebra, its $SU(2)$ gaugepotential is expressed as flat connection. As an example of application, weobtain the inner topological structure of second Chern number by $SU(2)$ flatconnection method. It's well known that if magnetic monopole exists inelectrodynamics, its Wu-Yang potential is indispensable in $U(1)$ invariantelectromagnetic field. In $2$-dim magnetic materials, we prove that if magneticskyrmion exists, its integral kernel must be $U(1)$ Wu-Yang curvature, whereits $U(1)$ Wu-Yang potential is the projection of $SU(2)$ flat connection on$su(2)$ local Cartan subalgebra. The magnetic skyrmion can be created byperforming concrete $SU(2)$ local gauge transformation to $su(2)$ Cartansubalgebra $\sigma_3$. The components of the $U(1)$ Wu-Yang curvaturecorrespond to the emergent electromagnetic field of magnetic skyrmion

The Wu-Yang potential of Magnetic Skyrmion from SU(2) Flat Connection