Orbifold quantum K-theory


Givental and Lee introduced quantum K-theory, a K-theoretic generalization of Gromov–Witten theory. It studies holomorphic Euler characteristics of coherent sheaves on moduli spaces of stable maps to given target spaces. In this talk, I will introduce the quantum K-theory for orbifold target spaces which generalizes the work of Tonita-Tseng. In genus zero, I will define a quantum K-ring which specializes to the full orbifold K-ring introduced by Jarvis-Kaufmann-Kimura. As an application, I will give a detailed description of the quantum K-ring of weighted projective spaces, which generalizes a result by Goldin-Harada-Holm-Kimura. This talk is based on joint work with Yang Zhou.