Georgia Institute of Technology College of Sciences

Given a space X, one can study various "genera", which give cobordism invariants with interesting properties. In this talk, I will consider the case when X is the moduli space of quasimaps from a smooth projective curve C to a Nakajima quiver variety. I will present a number of results on the (twisted virtual equivariant) Hirzebruch genus and elliptic genus of such spaces. Such invariants are often determined by the case when C is genus zero. When the quiver variety is zero-dimensional, the quasimap moduli spaces generalize the variety parameterizing rank 0 quotients of a fixed vector bundle on C. In these cases, we can prove complete formulas which exhibit an a-postiori independence of the equivariant parameters, a phenomenon sometimes called "rigidity". This is based on work in progress with Reese Lance.