Elliptic genus, and its various generalizations, is one of the simplest numerical invariants of a scheme that one can consider in elliptic cohomology. I will present a topological condition which implies that elliptic genus is invariant under wall-crossing. It is related to Krichever-Höhn’s elliptic rigidity. Many applications are possible: to GIT quotients, moduli of sheaves, Donaldson-Thomas invariants, etc.