The Euler characteristic has the following property: for a fiber bundle \(F \to E \to B\), we have \(\chi(E) = \chi(F)\chi(B)\). Restricting the class of fibrations yields a broader family of multiplicative genera. In this way, the Landweber–Stong elliptic genus arises. Within a unified framework, I will mention its generalizations, including the universal complex elliptic genus by Höhn and Krichever. The universal elliptic genus can be treated as a function from the complex cobordism ring to the ring of quasi Jacobi forms. The elliptic genus of Calabi–Yau manifolds has special properties.
