James Simons worked on differential geometry and geometric invariants. With Shiing-Shen Chern, he introduced the secondary characteristic forms now associated with Chern-Simons forms.[ref]
Characteristic forms and geometric invariants by Shiing-Shen Chern and James Simons. Original byline, introduction and equation 3.1
The construction produces a form whose exterior derivative is a characteristic curvature form. The introduction explains how a search for a combinatorial formula for a number obtained from a Pontryagin class led to an interesting boundary term. That term became a geometric object in its own right, illustrating how an obstruction in one calculation can generate a new invariant.[ref]
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