A combinatorial Chern-Weil theorem for 2-plane bundles with even Euler characteristics
The main result gives a formula \(\chi (\xi)=C(\xi)\) for a 2-plane bundle \(\xi\) over a surface where \(\chi\) (\(\xi\)) is the Euler class (which is assumed to be even) and C(\(\xi\)) is a combinatorial Chern-Weil class, the latter being defined in terms of triangulations, normal vectors and classifying maps for \(\xi\). The curvature of polyhedral surfaces is expressed by exterior angles, the combinatorial Gauss map, and by areas of spherical geodesic triangles.
scientific article; zbMATH DE number 4192669
scientific article