 This led to certain other problems concerning formula_1-actions on manifolds, which could be solved by Ochanine by the introduction of elliptic genera.In turn, Witten related these to (conjectural) index theory on free loop spaces.Elliptic cohomology, invented in its original form by Landweber, Stong and Ravenel in the late 1980s, was introduced to clarify certain issues with elliptic genera and provide a context for (conjectural) index theory of families of differential operators on free loop spaces.