= Boundary winding representation of Yang-Mills topological charge
{title2=$\frac1{8\pi^2}\int\operatorname{tr}(F\wedge F)=\deg g$}
For an anti-Hermitian <SU(2)> connection on $\mathbb R^4$ tending to $g^{-1}dg$ at infinity, the <Chern-Simons 3-form> and <Maurer-Cartan equation> give $(8\pi^2)^{-1}\int\operatorname{tr}(F\wedge F)=-(24\pi^2)^{-1}\int_{S^3}\operatorname{tr}(g^{-1}dg)^3=\deg g$. This is the second-Chern convention with the boundary orientation. Defining instanton charge with the opposite trace sign reverses this integer.
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