Elliptic cohomology

Summary

An elliptic cohomology theory is a generalized cohomology theory whose formal group law comes from an elliptic curve. Ordinary cohomology corresponds to the additive group and complex K-theory to the multiplicative group; elliptic curves are the next family of one-dimensional group varieties. Elliptic cohomology theories detect height $2$ phenomena in chromatic homotopy theory. They are tied to elliptic genera of manifolds and to topological modular forms.