Gauss-Bonnet: int_M K dA + oint k_g ds = 2 pi chi(M); topological-invariance of curvature

Gauss-Bonnet framework (Gauss 1827 Disquisitiones generales circa superficies curvas; Bonnet 1848 J Ec Polytech 19, 1; Chern 1944 Ann Math 45, 747 generalised version). Setup: for a compact oriented 2-Riemannian manifold M with smooth…