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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]

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]

Shiing-Shen Chern developed methods connecting curvature, differential geometry and topological invariants. His joint work with James Simons constructs secondary characteristic forms from connections.^[ref]

The key relation expresses a characteristic curvature form as an exterior derivative on an appropriate total space. Its primitive carries geometric information beyond the original cohomology class. The resulting Chern-Simons forms connects local differential forms with global invariants and later applications in mathematical physics.^[ref]