 However, the advantage of the cohomology groups is that there is a natural product, which is analogous to the observation that one can multiply pointwise a "k"-multilinear form and an "l"-multilinear form to get a ("k" + "l")-multilinear form.The ring structure in cohomology provides the foundation for characteristic classes of fiber bundles, intersection theory on manifolds and algebraic varieties, Schubert calculus and much more.To any group is associated its Burnside ring which uses a ring to describe the various ways the group can act on a finite set.